The box plot represents the midterm scores of the students in a class:

The Box Plot Represents The Midterm Scores Of The Students In A Class:

Answers

Answer 1

The percent of the students that had a score greater than or equal to 50 include the following: C. 75%.

What is a box-and-whisker plot?

In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the given box-and-whisker plot, the five-number summary for the given data set include the following:

Minimum (Min) = 30.First quartile (Q₁) = 50.Median (Med) = 60.Third quartile (Q₃) = 90.Maximum (Max) = 100.

For the required percent, we have;

Q₁ = 50:

Percent = 100% - 25%

Percent = 75%

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Related Questions

if you have not opened the cell phones datafile, see the data section above. to answer the research question we need to determine the proportion of the sample that owns a smartphone. we can do this with statcrunch. in the previous activity we identified each of the following. variable needed to answer the research question: cell (a categorical variable) appropriate numerical summary: percentage (proportion) appropriate graph: pie chart use statcrunch to create a pie chart with the appropriate percentages. (directions) what proportion of the sample owns a cell phone? enter your sample proportion rounded to the nearest percent. for example enter 83 not 0.825 or 82.5. do not include the % symbol.

Answers

The proportion of the sample that owns a smartphone was 83%.

The research question asked what proportion of the sample owns a smartphone.

To answer this question, we used a categorical variable called “cell” and created a pie chart with the appropriate percentages. We then determined the percentage of the sample that owns a smartphone and rounded it to the nearest percent.

In this case, the proportion of the sample that owns a smartphone was 83%.Identify the variable needed to answer the research question: Cell (categorical variable)The appropriate numerical summary: Percentage (proportion)A pie chart with the appropriate percentages in StatCrunch.

The percentage of the sample that owns a smartphone. The percentage to the nearest percent. The research question: 83% of the sample owns a smartphone.

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Jamal's dog buried a bone 4 feet below the ground. Which equation best represents the depth of the bone in feet? I will give 30 points

Answers

The linear equatiοn that best represents the depth οf the bοne in feet is x-4.

What is a linear equatiοn, exactly?

A linear equatiοn is an algebraic equatiοn that represents a straight line οn a graph. It cοnsists οf variables raised tο the first pοwer, cοnstants, and cοefficients, and can be written in the fοrm y = mx + b, where m is the slοpe οf the line and b is the y-intercept.

Linear equatiοns can be used tο mοdel a wide range οf real-wοrld situatiοns, including the relatiοnship between twο variables that are directly prοpοrtiοnal tο each οther. They are fundamental tο the study οf algebra and are widely used in many fields, including physics, engineering, and ecοnοmics.

Nοw,

The equatiοn that represents the depth οf the bοne in feet is:

depth =x-4  (As Jamal's dοg buried a bοne 4 feet belοw the grοund)

where x is the distance in feet frοm the surface οf the grοund.

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Complete Question :

Question:
The electrical resistance (R) of a
wire varies directly as its length (I)
and inversely as the square of its
diameter (d). A wire with a length
of 5.0 m and a diameter of 0.25
cm has a resistance of 20 Q
(ohms). Find the electrical
resistance in a 10 m long wire that
has twice the diameter.

Answers

Answer:

Step-by-step explanation:

R = [tex]\frac{KL}{d^{2} }[/tex] ------ equ.1

given R= 2O, L = 5.Om = 500cm, d = 0.25cm. substituting the given data into the above equation,

20 = [tex]\frac{500k}{(0.25)^{2} }[/tex]

20 = [tex]\frac{5.0K}{0.0625}[/tex]

50OK = 20 x 0.0625

K = [tex]\frac{20*0.0625}{500}[/tex]

K = 0.0025

substituting  value of K into equ. 1

R = [tex]\frac{0.0025L}{d^{2} }[/tex]

(from the second part of question, R = 10m = 1000cm, d = 2 x 0.25 = 0.5cm)

R = [tex]\frac{0.0025*1000}{(0.5)^{2} }[/tex]

R = 10

10. At noon, two tracking stations on Earth that are 20 km apart measure the angles of elevation of a rocket that
was launched carrying a weather satellite into outer space. From the station A, the angle of elevation is 41° and
from station B it is 75°. Find the altitude of the rocket to the nearest km.

Answers

The approximate altitude of the rocket is 34.45 km (rounded to the nearest kilometer).

How to find the altitude of rocket?Create two right triangles, one for each tracking station, with the distance between the stations on the adjacent side and the rocket's height on the other side.For each station, relate the triangle's sides and elevation angle using the tangent function.To get the height of the rocket for each station, substitute the provided angle of elevation data into the tangent function.To get the estimated altitude of the rocket, take the average of the two determined altitudes.To get the final solution, round the result to the closest kilometre.

Given:

Angle of elevation from station A = 41°

Angle of elevation from station B = 75°

Distance between station A and station B = 20 km

Using the tangent function to calculate the altitude 'h' for each station:

For station A:

h = 20 * tan(41°) ≈ 17.39 km (rounded to two decimal places)

For station B:

h = 20 * tan(75°) ≈ 74.64 km (rounded to two decimal places)

Taking the average of the two altitudes,

(h from station A + h from station B)/2 = (17.39 + 74.64)/2 ≈ 34.45 km (rounded to two decimal places)

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at their highest rate, the wildfires which ravaged california were estimated to have consumed the equivalent of one football field per three seconds, over a 20-hour period. if a football field is 360 feet long and 160 feet wide, how many square inches per minute, was the fire burning at its highest rate? be sure to include units with your answer.

Answers

the fire was burning at its highest rate at approximately 165,888,000 square inches per minute.

To find the square inches per minute that the fire was burning at its highest rate, we need to first find the total square footage of a football field, which is 360 feet x 160 feet = 57,600 square feet.

Since there are 12 inches in a foot, we can convert the square footage to square inches by multiplying by 12^2 (or 144).

57,600 square feet x 144 square inches per square foot = 8,294,400 square inches in one football field.

Next, we can find how many football fields the fire consumed in 20 hours by dividing the number of seconds in 20 hours (20 x 60 x 60 = 72,000 seconds) by 3 seconds per football field:

72,000 seconds ÷ 3 seconds per football field = 24,000 football fields consumed.

Finally, we can find the total square inches consumed by multiplying the number of football fields by the square inches in one football field:

24,000 football fields x 8,294,400 square inches per football field = 199,065,600,000 square inches consumed in 20 hours.

To find the square inches per minute, we can divide the total square inches consumed by the number of minutes in 20 hours (20 x 60 = 1,200 minutes):

199,065,600,000 square inches consumed ÷ 1,200 minutes = 165,888,000 square inches per minute.

Therefore, the fire was burning at its highest rate at approximately 165,888,000 square inches per minute.

Units: square inches per minute.

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At its highest rate, the fire was burning 16,588,800,000 square inches per minute.


First, find the area of one football field in square feet.
Area = length × width
Area = 360 feet × 160 feet
Area = 57,600 square feet
Convert the area to square inches. (1 foot = 12 inches)
Area = 57,600 square feet × (12 inches/foot) × (12 inches/foot)
Area = 829,440,000 square inches
Calculate the number of football fields burned per minute.
Since one football field was burned every 3 seconds,

we can find the number of football fields burned in a minute by dividing 60 seconds by 3 seconds.
Number of football fields burned per minute = 60 seconds / 3 seconds = 20 football fields
Calculate the total area burned per minute in square inches.
Area burned per minute = 20 football fields × 829,440,000 square inches/football field
Area burned per minute = 16,588,800,000 square inches.

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the alvin secretarial service procures temporary office personnel for major corporations. they have found that 50% of their invoices are paid within ten working days. a random sample of 10 invoices is checked. what is the probability that more than 7 of the invoices will be paid within ten working days? round your answer to four decimal places.

Answers

The probability that more than 7 of the invoices will be paid within ten working days is 0.8281

This is a binomial distribution problem where:

n = 10 (sample size)

p = 0.5 (probability of success, i.e., an invoice being paid within ten working days)

We need to find the probability of getting more than 7 invoices paid within ten working days, i.e., P(X > 7), where X is the number of invoices paid within ten working days.

Using the binomial probability formula, we get:

[tex]P(X > 7) = 1 - P(X ≤ 7)[/tex]

=[tex]1 - ∑(i=0 to 7) [nCi * p^i * (1-p)^{(n-i)][/tex]

where nCi is the number of ways to choose i items from n items, given by [tex]nCi = n! / (i! * (n-i)!).[/tex]

Calculating the above expression, we get:

[tex]P(X > 7) = 1 - [10C0 * 0.5^0 * 0.5^10 + 10C1 * 0.5^1 * 0.5^9 + ... + 10C7 * 0.5^7 * 0.5^3][/tex]

[tex]= 1 - 0.1719[/tex]

[tex]= 0.8281[/tex]

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you are in charge of conducting a very important study on the efficacy of imitrex on migraine sufferers. you ask 25 women to test this drug. each of the 25 women is given 'excedrin for migraines' immediately after the onset of their first migraine, after which you measure the time it takes for the headache to subside. after the onset of their second migraine, you give them imitrex and again measure the time it takes for the headache to subside. assuming the data are normally distributed, which is the most appropriate statistical test to determine if imitrex works better than excedrin at eliminating migraines?

Answers

If the p-value obtained from the paired t-test is less than the predetermined level of significance (usually 0.05), then it can be concluded that there is a statistically significant difference between the two treatments, and that imitrex is more effective than excedrin at eliminating migraines.

To determine if Imitrex works better than Excedrin at eliminating migraines in your study, the most appropriate statistical test to use is the Paired Samples t-test.

This test is suitable because:
We have two related samples: the same 25 women are given both Excedrin and Imitrex, so their response times are paired.
We're comparing the mean response times between two treatments, which requires a t-test.

The data is assumed to be normally distributed.
To conduct the Paired Samples t-test, follow these steps:
Calculate the difference in response times for each woman (Imitrex time - Excedrin time).

Calculate the mean of these differences.

Calculate the standard deviation of the differences.

Determine the degrees of freedom (25 women - 1 = 24).

Using the mean, standard deviation, and degrees of freedom, calculate the t-statistic.
Compare the t-statistic to the critical value from the t-distribution table, using your chosen significance level (e.g., 0.05).
If the t-statistic is greater than the critical value, reject the null hypothesis, concluding that there's a significant difference between the effectiveness of Imitrex and Excedrin for migraine relief.

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To determine if Imitrex works better than Excedrin, the most appropriate statistical test to use would be a "paired t-test."

We are comparing the efficacy of Imitrex and Excedrin for Migraine in the same group of 25 women, with each woman acting as her own control. You are measuring the time it takes for the headache to subside after administering each drug. To determine if Imitrex works better than Excedrin, the most appropriate statistical test to use would be a "paired t-test."

Step-by-step explanation:

1. Record the time it takes for the headache to subside after administering Excedrin and Imitrex to each woman.
2. Calculate the difference in time for each woman between the two drugs.
3. Compute the mean and standard deviation of these differences.
4. Perform a paired t-test to compare the mean difference to 0 (no difference between the two drugs).
5. Assess the p-value obtained from the t-test. If the p-value is less than the significance level (usually 0.05), then you can conclude that there is a statistically significant difference between the two drugs, suggesting that Imitrex works better than Excedrin in eliminating migraines.

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using the partial f-test, determine the contribution of x7 to the model. how is this partial f statistic related to the t test for 7 calculated in part c above?

Answers

To determine the contribution of predictor X7 to a multiple linear regression model with p predictors and n observations, the partial F-test can be used to calculate the partial F-statistic for X7. This partial F-statistic is related to the t-test calculated for X7 in the same model, as the square of the t-statistic for X7 is equal to the partial F-statistic for X7.

To calculate the partial F-statistic for X7, you first fit the full model with all p predictors and record the residual sum of squares (RSS). Then, you fit a reduced model without X7 and record the residual sum of squares for this model (RSSr). The partial F-statistic for X7 is calculated as (RSSr - RSS) / q / RSS, where q is the number of predictors in the reduced model (excluding X7). This statistic follows an F distribution with 1 numerator degree of freedom and q denominator degrees of freedom.

The partial F-statistic is related to the t-test calculated for X7 in the same model because the square of the t-statistic for X7 is equal to the partial F-statistic for X7. Specifically, t^2 = partial F, where t is the t-statistic for the coefficient of X7 in the full model.

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--The complete question is, Suppose you have a multiple linear regression model with p predictors and n observations. Using the partial F-test, you want to determine the contribution of a particular predictor, say X7, to the model. How do you calculate the partial F-statistic for X7 and how is it related to the t-test calculated for X7 in the same model?--

Suppose a trapezoid is defined as a quadrilateral with at least one pair of parallel sides. How would the quadrilateral “family tree” change?

Answers

The addition of trapezoids as a distinct category of quadrilaterals would modify the hierarchical structure of the "family tree" of quadrilaterals

What are parallel lines?

Parallel lines are two lines in a plane that never intersect. This means that they maintain the same distance between each other at all points. Parallel lines have the same slope and will never cross each other, no matter how far they are extended.

If we consider a trapezoid as a quadrilateral with at least one pair of parallel sides, it would affect the classification of other quadrilaterals in the "family tree". Specifically, the hierarchy of quadrilaterals would change as follows:

Quadrilaterals would be divided into two main groups: trapezoids and non-trapezoids.

Trapezoids would be further subdivided into isosceles trapezoids, where the non-parallel sides have the same length, and non-isosceles trapezoids, where the non-parallel sides have different lengths.

Non-trapezoids would be further divided into four subgroups: parallelograms, rectangles, rhombi, and squares.

Parallelograms would be defined as quadrilaterals with opposite sides parallel.

Rectangles would be defined as quadrilaterals with four right angles and opposite sides parallel.

Rhombi would be defined as quadrilaterals with all sides equal in length.

Squares would be defined as quadrilaterals that are both rectangles and rhombi.

Overall, the addition of trapezoids as a distinct category of quadrilaterals would modify the hierarchical structure of the "family tree" of quadrilaterals, and provide a more precise and comprehensive way of classifying these shapes based on their properties.

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this lesson will focus on finding the perimeter of rectangles. truefalse\

Answers

Answer:

Step-by-step explanation:

false

Given a circle has a center at (-6, 14) and a diameter of 30, write the equation of the circle

Answers

Answer:

The center of the circle is at (-6, 14), and the radius is 15, so we have this equation:

[tex] {(x + 6)}^{2} + {(y - 14)}^{2} = 225 [/tex]

Pam is a hairdresser. Before her lunch break, she gave 2 haircuts and colored the hair of 1 client in 83 minutes. After lunch, she gave 1 haircut and colored the hair of 3 clients in 164 minutes. How long does it take for Pam to perform each type of service, assuming the amount of time doesn’t vary from client to client?

Answers

Answer: Let's assume that it takes Pam x minutes to give a haircut and y minutes to color hair.

From the information given, we can create two equations:

2x + y = 83 (Pam gave 2 haircuts and colored the hair of 1 client in 83 minutes)

1x + 3y = 164 (Pam gave 1 haircut and colored the hair of 3 clients in 164 minutes)

To solve for x and y, we can use elimination method or substitution method. Let's use substitution method.

From the first equation, we can solve for y in terms of x:

y = 83 - 2x

Substituting this into the second equation, we get:

1x + 3(83 - 2x) = 164

Simplifying and solving for x, we get:

x = 30

Substituting this value of x into either of the two equations, we can solve for y:

2(30) + y = 83

y = 23

Therefore, it takes Pam 30 minutes to give a haircut and 23 minutes to color hair.

Step-by-step explanation:

URGENT PLEASE ANSWER 100 POINTS
Using the functions below, analyze the change in the key features from f(x) to g(x).

Answers

5x y= 3xy so it is the awesome

The solid below is dilated by a scale factor of 1/2. Find the volume of the
solid created upon dilation.
24
26
10
34

Answers

Answer: 4080

Step-by-step explanation:

First you have to find the area of the triangle. 24*10 = 240. 240/2 = 120. Then you multiply the area of the triangle and multiply it by 34. 120 * 34 = 4080. This means the answer is 4080

some girls who excelled at math/science in elementary school, during puberty may fear focusing on these may limit popularity or attractiveness as girls.

Answers

It is essential to encourage and support these girls to continue pursuing their interests and talents in math and science, as excelling in these fields can lead to successful careers and personal growth.

It is unfortunate that some girls may fear focusing on math and science during puberty due to concerns about popularity or attractiveness. However, it is important to remember that excelling in these subjects can lead to numerous opportunities and career paths in the future. It is also important to note that intelligence and academic achievement should be celebrated and valued regardless of gender stereotypes. Schools can play a role in promoting the importance of STEM subjects and encouraging girls to pursue their interests in these areas.

It has been observed that some girls who excelled in math and science during elementary school may develop concerns during puberty that focusing on these subjects might limit their popularity or attractiveness as girls. This could be due to societal stereotypes or peer pressure, which might influence their academic choices and priorities. It is essential to encourage and support these girls to continue pursuing their interests and talents in math and science, as excelling in these fields can lead to successful careers and personal growth.

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It is essential to encourage and support these girls to continue pursuing their interests and talents in math and science, as excelling in these fields can lead to successful careers and personal growth.

It is unfortunate that some girls may fear focusing on math and science during puberty due to concerns about popularity or attractiveness. However, it is important to remember that excelling in these subjects can lead to  and career paths in the future. It is also important to note that intelligence and academic achievement should be celebrated and valued regardless of gender stereotypes. Schools can play a role in promoting the importance of STEM subjects and encouraging girls to pursue their interests in these areas.

It has been observed that some girls who excelled in math and science during elementary school may develop concerns during puberty that focusing on these subjects might limit their popularity or attractiveness as girls.

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Factor this expression as far as possible:
-385y

I need help with math, its hard

Answers

Answer:

-5y * 77

Step-by-step explanation:

The largest number we can factor out is 5. Therefore:

-385y

= -5y * 77

The 16 factors of -385 are:

1, 5, 7, 11, 35, 55, 77, 385

-1, -5, -7, -11, -35, -55, -77, -385

The factor pairs of -385 are:

1 × -385 = -385

5 × -77 = -385

7 × -55 = -385

11 × -35 = -385

35 × -11 = -385

55 × -7 = -385

77 × -5 = -385

385 × -1 = -385


Hope my answer helps you✌️

Mark BRAINLIEST

Red=10
blue=8
yellow=5
what is the ratio of red balls to blue balls?

Answers

Answer:1.25

Step-by-step explanation:

it just math

Find the measure of the line segment indicated, assume that lines which appear tangent, are tangent.
Find FS
Possible answers —>
A. 17
B. 21
C. None of the other answers are correct
D. 18
E. 45

Answers

The value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

What is the properties of intersecting chords

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

UF × FS = VF × FT

8(10x - 1) = 9 × 16

80x - 8 = 144

80x = 144 + 8 {collect like terms}

80x = 152

x = 152/80 {divide through by 80}

x = 1.9

FS = 10(1.9) - 1 = 18

Therefore, the value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

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Mr. Lowe is a school librarian. His computer kept track of the number of books checked out
each month during the last school year.
Books checked out

4,247. 4,983. 6,214. 7,500. 3,500. 2,500. 5,000. 3,876. 4,753. 2,712.

Which box plot represents the data?

Answers

Answer:

  A (top)

Step-by-step explanation:

You want to know which box plot represents the data in the given list.

Median

The difference between the box plots is the location of the median.

When the data is sorted into order, it is ...

  {2500, 2712, 3500, 3876, 4247, 4753, 4983, 5000, 6214, 7500}

There are an even number of elements in this list, so the median is the average of the middle two:

  median = (4247 +4753)/2 = 9000/2 = 4500

The median is represented by the line inside the box of the box plot. The plot with its median at 4500 is the top one (shown in the attachment).

The top box plot represents the data.

<95141404393>

A fair spinner, with four equally-sized sections, and a fair, two-sided coin are shown.

At the same time, the spinner is spun and the fair coin is tossed in the air.
Complete the statement by typing a fraction in the blank space.

The theoretical probability that the spinner will land on green and the coin will land on tails is

Answers

The probability of both events happening at the same time: P(green and tails) = P(green) x P(tails) = (1/4) x (1/2) = 1/8

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

1/8.

There are four equally-sized sections on the spinner, so the probability of landing on green is 1/4. There are two equally likely outcomes when flipping a coin, so the probability of landing on tails is 1/2. Since the spinner and coin toss are independent events, we can multiply their probabilities to get the probability of both events happening at the same time: P(green and tails) = P(green) x P(tails) = (1/4) x (1/2) = 1/8.

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the mean age of 5 students whose ages are 8,x,13,12,and 10 is 10. calculate the value of x in years​

Answers

Answer:

x = 7 years

Step-by-step explanation:

The mean (M) is defined as the average of the sum of all the data points in a set:

[tex]M=\frac{r_{1}...r_{n} }{n}[/tex]

Thus, since there are five data points and we're given the mean, we can use the following formula to find x:

[tex]M=10\\10=\frac{(8+x+13+12+10)}{5}\\ 50=43+x\\7=x[/tex]

In ΔHIJ, the measure of ∠J=90°, HI = 6. 7 feet, and JH = 4. 8 feet. Find the measure of ∠I to the nearest degree

Answers

The measure of angle I in the triangle HIJ using given measurements is equal to 46.05 degrees.

In the triangle HIJ,

The measure of angle J is equal to 90 degrees.

This implies ,

HI is the hypotenuse.

JH is the opposite side to angle I.

In triangle HIJ,

Using trigonometric ratio we get,

sin ∠I = Opposite side / Hypotenuse

Substitute the values we have,

⇒ sin ∠I = 4.8 / 6.7

⇒ sin ∠I = 0.72

Now , take sin⁻¹ both the side of the equation we get,

⇒sin⁻¹(sin ∠I) = sin⁻¹( 0.72 )

Here sin⁻¹(sin ∠I) = ∠I

⇒∠I = sin⁻¹( 0.72 )

⇒∠I = 46.05 degrees

Therefore, the measure of angle I is equal to 46.05 degrees.

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1. The area of a rectangle can be represented by a
quadratic function. You are given a rectangle with a length
that is 3 inches more than four times the width, w. Choose
all the answers that give the area as a function of the
width
a) A(w)=w(4+3w)
b) A(w)=w(3+4w)
c) A(w)=4w+3w²
d) A(w)=4w²+3w
-7

Answers

The expression that gives the area as a function of the width is 4w²+3w.( option B)

What is area of a rectangle?

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The area of a rectangle is expressed as ;

A = l×w, where l is the length and w is the width.

Since the length is 3 inches more than four times the width, then;

l = 3+4w

Representing 3+w for l in the area formula, then we have;

A = (3+4w)(w)

A = 4w²+3w

therefore the expression that represents the area is 4w²+3w

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the variance is equal to the . a. squared value of the standard deviation b. inverse value of the standard deviation c. absolute value of the standard deviation d. square root of the standard deviation

Answers

The variance is equal to the squared value of the standard deviation.(Option a)

The variance is a measure of how spread out a set of data is. It is calculated by taking the average of the squared differences of each data point from the mean. The standard deviation, on the other hand, is the square root of the variance and measures the spread of data in relation to the mean.

Therefore, the variance is equal to the squared value of the standard deviation. Mathematically, Var(X) = σ^2, where Var(X) is the variance and σ is the standard deviation.

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PLEASE HELP ME IM NOT GOOD AT MATH AND don’t understand!!

Answers

The total volume of the cylindrical can is given as follows:

C) 24.54 in³.

How to obtain the volume of a cylinder?

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

The parameters for this problem are given as follows:

h = 5 in.r = 1.25 in.

Hence the volume of the cylinder is obtained as follows:

V = π x 1.25² x 5

V = 24.54 in³.

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40000 is divided by the smallest number so that the result is a perfect cube. find the cube root of the resulting number.

Answers

The Cube root of the resulting number is 8.

The smallest number that 40000 can be divided by so that the result is a perfect cube, we need to factorize 40000 into its prime factors:

[tex]40000 = 2^6 \times 5^4[/tex]

To make this a perfect cube, we need to ensure that the powers of each prime factor are multiples of 3.

The smallest number we can divide 40000 by so that the result is a perfect cube is:

[tex]40000 = 2^6 \times 5^4[/tex]

Now we can find the cube root of the resulting number:

[tex]3\sqrt (40000 \div 100) = 3\sqrt400 = 8.[/tex]

Factories 40000 into its prime components in order to determine.

The least number that the result may be divided by while still producing a perfect cube.

The powers of each prime factor must be multiples of three in order for this to be a perfect cube.

The least number that 40000 may be divided by to produce a perfect cube is:

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Find the radius of convergence, R, of the series. [infinity]

n = 2
(x + 8)n
8n ln(n)

Answers

The radius of convergence is 4.

To find the radius of convergence, R, of the collection, we can use the ratio test:

[tex]lim_n→∞ |(a_(n+1)/[/tex][tex]a_n)|[/tex]

[tex]lim_n→∞ |(a_{(n+1})/[/tex]

[tex]= lim_n→∞ |(x+8) / 4| * |ln(n+1) / ln(n)|[/tex]

For the series to converge, this limit need to be less than 1. therefore, we've:

[tex]|(x+8) / 4| * lim_n→∞ |ln(n+1) / ln(n)| < 1[/tex]

For the reason that[tex]lim_n→∞ |ln(n+1) / ln(n)| = 1[/tex], we will simplify this to:

|(x+8) / 4| < 1

Taking the absolute cost under consideration, we have cases:

Case 1: (x+8)/4 < 1

In this case, we have x < -4.

Case 2: (x+8)/4 > -1

In this case, we have x > -12.

Consequently, the radius of convergence is the distance from the center of the collection (x = -8) to the closest endpoint of the c language (-12 on the left and -4 at the right):

R = min{8, 4} = 4

So, 4 is the radius of convergence.

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Question 8 of 10
f(x) = x2. What is g(x)?
g(x)
5
f(x)
D. g(x)-
(2, 1):
5
A g(x) = 4x²
OB. g(x)=x²
O C. g(x)-1x²

Answers

Thus, the new function g(x) on the graph is the result of dilation with the scale factor of 2. g(x) = 4x².

Explain about the dilation of function:

When a function is drawn closer to or farther away from an axis, it is said to have "dilated."

The connection between the two functions shown in the above graph can be explained in two different ways. Either:To create the dashed line, the solid line has either been "dilated vertically by a factor of 2" or the solid line has been "dilated vertically by the a factor of 0.5".

Given data:

Parent function f(x) = x²

New function g(x) = ?

From the given graph, consider the point (2,1) on the graph of g(x) function.

For the same value of y = 1 unit, x = 1 on the graph of f(x)

Thus, x ---> 2x (dilation by the scale factor of 2)

Now function:

g(x) = (2x)²

g(x) = 4x²

Thus, the new function g(x) on the graph is the result of dilation with the scale factor of 2. g(x) = 4x².

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Can someone help me with this?

Answers

The value of angle G is  31⁰.

The value of line GF is 5.

The value of X is 13.

The value of Y is 2.

What is the value of angle G?

The value of angle G is calculated as follows;

4x + 7 = 5x - 6

4x - 5x = - 6 - 7

-x = -13

x = 13

Angle H = angle F = 4x + 7

= 4(13) + 7

= 59⁰

Angle G = ¹/₂ (180 - 2x59)

Angle G = ¹/₂(180 - 118)

Angle G = 31⁰

The value of Y is calculated as follows;

y + 3 = 2y + 1

y - 2y = 1 - 3

-y = -2

y = 2

GF = 2y + 1

GF = 2x2 + 1 = 5

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If f(x) = 5x - 6, which of these is the inverse of f(x)?

A. f^-¹(x) = x/5 +6

B. f^-¹(x) = x/5 -6

C. f^-¹(x) = x+6/5

D. F^-¹(x) = x-6/5

Answers

To find the inverse of a function, we need to swap the positions of x and y and then solve for y. In other words, we replace f(x) with y and then solve for x.

So, let's start by swapping x and y in the function f(x) = 5x - 6:

x = 5y - 6

Next, we'll solve this equation for y:

x + 6 = 5y

y = (x + 6)/5

Therefore, the inverse of f(x) is f^-1(x) = (x + 6)/5, which is option C.

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