Suppose you want to save $7,500 to go on a dream vacation in three years. You can save for your vacation by either depositing one single lump of money into a savings account and letting it accumulate interest or by making regular monthly payments.

Since the sample size is relatively small (n=25), the shape οf the histοgram may nοt perfectly reflect the underlying distributiοn οf the pοpulatiοn.

The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.

The range οf the data is the difference between the maximum and minimum values:

Maximum value: 5.4

Minimum value: 3.4

Range: 5.4 - 3.4 = 2.0

Next, we divide the range by the desired number οf classes tο find the class width:

Class width = 2.0 / 6 = 0.3333 (rοunded tο 0.4)

Based οn the given data, we can expect the histοgram tο be apprοximately bell-shaped, with a peak arοund the middle classes (4.0-4.8) and fewer pencils in the extreme classes (3.4-3.8 and 5.4-5.8).

Hοwever, since the sample size is relatively small (n=25), the shape οf the histοgram may nοt perfectly reflect the underlying distributiοn οf the pοpulatiοn.

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Answer: The decay rate is 8.4%, which means that the sample will have 91.6% of its original mass after one year, 91.6% of that amount after two years, and so on.

Therefore, we can write the relationship between y and t as:

y = 600 * (0.916)^t

This is an exponential decay function, where the initial value is 600 milligrams and the decay factor is 0.916 (1 minus the decay rate of 8.4%). As time t increases, the mass of the sample y decreases exponentially.

Step-by-step explanation:

Answer:

The correct answer:

D. (h, k)

Answer:

what is it

Step-by-step explanation:

Note that the journal for the above transaction is attached accordingly.

The journal entry records the purchase of land for $445,000, demolition expense of $37,600, land improvement cost of $55,583, building construction cost of $1,402,600 and lighting and paving cost of $88,536, all paid in cash.

Therefore, the amounts are debited to their respective accounts and credited to cash.

The total credit amount is equal to the total debit amount, ensuring the accounting equation remains in balance.

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the distance she hiked each day, we need to calculate the difference between the distance she hiked on consecutive days. Yolanda increased the distance she hiked by 1 mile each day.

To find the increase in the distance Yolanda hiked each day, we need to calculate the difference between the distance she hiked on each consecutive day.

The distance Yolanda hiked each day for the first three days can be represented as:

Day 1: d miles

Day 2: [tex]d + 1[/tex]  miles

Day 3:  [tex]d + 2[/tex] miles

The increase in distance from day 1 to day 2 is  [tex](d + 1) - d = 1[/tex]   mile.

The increase in distance from day 2 to day 3 is   [tex](d + 2) - (d + 1) = 1[/tex] mile.

Therefore, Yolanda increased the distance she hiked by 1 mile each day.

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Answer:

Step-by-step explanation:

11P3=11×10×9=990

[tex]11C_{3}=\frac{11 \times 10 \times 9}{3 \times 2 \times 1} =165[/tex]

Answer:

There were 60 audience members at the seminar.

Step-by-step explanation:

Let's assume that the total number of audience members at the seminar is "x".

From the given information, we know that:

2/5 of the audience were students, so the number of students was (2/5)x

3/10 of the audience were retirees, so the number of retirees was (3/10)x

The rest were professionals, so the number of professionals was x - (2/5)x - (3/10)x = (1/10)x

We also know that there were 18 more students than professionals, so:

(2/5)x - (1/10)x = 18

Multiplying both sides by 10, we get:

4x - x = 180

Simplifying, we get:

3x = 180

x = 60

Therefore, there were 60 audience members at the seminar.

Remark

I take it the semicircles cover the full width of the paper.

So the radius is [tex]24\div2 = 12 \ \text{cm}[/tex]

Since there are two of them, the area = a full circle.

Step One

Find the area of the rectangle before the cuts were made.

[tex]\text{Area = L} \times \text{W}[/tex]

[tex]\text{L = 30}[/tex]

[tex]\text{W = 24}[/tex]

[tex]\text{Area} = 30 \times 24 = 720 \ \text{cm}^2[/tex]

Step Two

Find the area of the circle cut outs.

[tex]\text{r} = 12[/tex]

[tex]\text{Area} = \pi \times \text{r}^2[/tex]

[tex]\text{Area} = 3.14 \times 12^2[/tex]

[tex]\text{Area} = 3.14 \times 144[/tex]

[tex]\text{Area} = 452.16 \ \text{cm}^2[/tex]

Step Three

Find the total area left

[tex]\text{Total Area Left = rectangle - circle}[/tex]

[tex]\text{Total Area Left} = 720 - 452.16[/tex]

[tex]\text{Total Area left} = 267.84 \ \text{cm}^2[/tex]   Answer

la cantidad buscada es 1440.

Para encontrar la cantidad dada el 15% de la misma, podemos usar una ecuación:

15% de x = 216

Podemos convertir el porcentaje a decimal dividiendo por 100:

0.15x = 216

Luego, para despejar x, podemos dividir ambos lados de la ecuación por 0.15:

x = 216 / 0.15

x = 1440

Por lo tanto, la cantidad buscada es 1440.

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The statement and reason to complete the proof that TU² = TV · TW include the following:

Statement                                  Reason_____

TU² = TV · TW                        cross product.

In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.

By applying the Tangent Secant Theorem to the given triangles after the definition of similarity step, we would cross-multiply as follows:

TU/TW = TV/TU                  definition of similarity

TU(TU) = TV(TW)                    cross product.

TU² = TV · TW                        cross product.

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Answer: Number 4 is the answer.

Hope this helps!

Another mathematical representation of how a rider on this Ferris wheel might move is :y =  cos(0.25x) + 40

Trigonometry is widely used in many fields, including physics, engineering, architecture, surveying, oceanography, and more. Here are several examples:

In astronomy and physics, trigonometry is used to compute the motions of moving objects, gauge the separations between planets and stars, and examine waves. Trigonometry is used in architecture and engineering to determine angles and distances for building structures like bridges and buildings.

In surveying, trigonometry is a tool used to determine angles and separations between points on the surface of the ground.

.

The function y = a cos(bx) + c, where an is the function's amplitude, b is its frequency, and c is its vertical shift, can be used to mimic the height of a rider on a Ferris wheel.

Given that the Ferris wheel's diameter in this instance is 60 meters, its radius is 30 metres. The Ferris wheel's center axle is 40 metres off the ground. This indicates that a rider is 70 metres above the earth when they are at the top of the Ferris wheel (30 + 40). A rider is 10 metres above the ground when they reach the bottom of the Ferris wheel. (40 - 30).

We can determine that the Ferris wheel's period is four minutes because it rotates once every four minutes. The following formula can be used to get our function's frequency:

f = 1/T, 1/4, and 0.25 Hz

Therefore, our function has a frequency of 0.25 Hz.

The vertical shift of our function is equivalent to 50% of the difference between a Ferris wheel passenger's maximum and minimum heights:

, c = (a_max + a_min) /2

c = (70 + 10) /2

c = 40

Therefore, 40 is the vertical shift of our function.

Finally, we must ascertain the function's amplitude. The difference between a Ferris wheel passenger's maximum and minimum heights is equal to half of the amplitude:

For example, c = (a_max + a_min) / 2 c = (70 + 10) / 2 c = 40

Therefore, 40 is the vertical shift of our function.

Finally, we must ascertain the function's amplitude. The difference between a Ferris wheel passenger's maximum and minimum heights is equal to half of the amplitude:

A=(a_max - a_min) / 2 A=(70 - 10) / 2 A=30

Therefore, our function has an amplitude of 30.

When you combine everything, you get:

Y equals a cos(0.25x) + 40

y = -25 cos(C), where C is the time in minutes since the motion started at position, is another potential mathematical model that could describe this motion. (0,-25).

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Answer:

The least possible degree is 5.

A rotation can be  transformation which turns a figure. It changes its position

what is rotation ?

Rotation is the act of turning or moving something around a fixed point or axis. It is a fundamental concept in mathematics, physics, and engineering, and is used to describe the movement of objects in space.

In the given question,

Rotation is the act of turning or moving something around a fixed point or axis. It is a fundamental concept in mathematics, physics, and engineering, A rotation can be  transformation which  turns a figure. It changes its position

when their is rotations it turns around its axis and their will be change in its position

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Answer:

the concentration of sugar in the tank after 10 minutes is approximately 0.056 pounds per gallon.

Step-by-step explanation:

Let's first calculate the amount of sugar that will be added to the tank during the 10 minutes:Amount of sugar added = rate of sugar * time = 2 pounds/minute * 10 minutes = 20 poundsThe initial amount of water in the tank is 300 gallons, and 20 gallons per minute are being added, so after 10 minutes, the amount of water in the tank will be:Amount of water in the tank = initial amount of water + rate of water * time = 300 gallons + 20 gallons/minute * 10 minutes = 500 gallonsTherefore, after 10 minutes, the total volume of the mixture in the tank will be 500 gallons, and the total amount of sugar in the tank will be 8 + 20 = 28 pounds.To find the concentration of sugar in the tank, we divide the total amount of sugar by the total volume of the mixture:Concentration of sugar = total amount of sugar / total volume of mixture = 28 pounds / 500 gallons ≈ 0.056 pounds per gallon

We can use the formula:

concentration = (total sugar added in pounds) / (total water in gallons)

First, we need to find out how much sugar is added in 10 minutes. Since sugar is being added at a rate of 2 pounds per minute , in 10 minutes, we will have:

total sugar added = 2 pounds/minute * 10 minutes = 20 pounds

Next, we need to find out how much water is in the tank after 10 minutes. Since water is being added at a rate of 20 gallons per minute , in 10 minutes, we will have:

total water added = 20 gallons/minute * 10 minutes = 200 gallons

Therefore, the total amount of water in the tank after 10 minutes is:

total water = 300 gallons (initial water) + 200 gallons (water added) = 500 gallons

Finally, we can calculate the concentration of sugar in the tank by plugging in the values:

concentration = total sugar added / total water

concentration = 20 pounds / 500 gallons

concentration = 0.04 pounds/gallon

Therefore, after 10 minutes, the concentration of sugar in the tank is 0.04 pounds per gallon.

The measures of the angles and arcs of the circle are;

The sum of the digits in the shaded = 1  + 3 + 7 + 2 + 3 + 4 + 6 = 26

26 - 14 = 12

Using the decoder wheel, we get; FVMMO

An arc is a portion or part of the circumference of the circle.

The arc angles from the diagrams indicates;

1. mPR = 90 + (90 - 67) = 113

2. mQST = mQR + mRST

mQST = 23 + 180 = 203

3. 8·x - 15 + (3·x + 8) = 180 (Linear pair angles)

11·x - 7 = 180

11·x = 187

x = 187/11 = 17

x = 17

4. LM = 3·x + 8

Therefore; LM = 3 × 17 + 8 = 59

LM = 59

5. m∠DAC = 156/2 = 78

6. mBC = 180 - 156 = 24

7. m∠ADB = 43

mAB = 43 × 2 = 86

mABD = 180 + 86 = 266

8. 2 × (7·x -3) = 17·x - 30

14·x - 6 = 17·x - 30

17·x - 14·x = 3·x = 30 - 6 = 24

x = 24/3 = 8

x = 8

9. m∠YZX = 7·x -3

m∠YZX = 7 × 8 - 3 = 53

m∠YZX = 53

10. m∠WXZ = 62/2 = 31

The angle formed by the intersection of WY and XZ is therefore;

mWZY = 180 - (2 × 53) + 63 = 137

mWXY = 180 - (2 × 31) + (17 × 8 - 30) = 224

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By answering the presented question, we may conclude that the answer of the triangle [tex]A = (3/2)h^2 - (1/2)h\\[/tex] =>  [tex]A(h) = (3/2)h^2 - (1/2)h[/tex]

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle may be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

x = 3h - 1

A = (1/2)bh

A = (1/2)xh

A = (1/2)(3h - 1)h

[tex]A = (3/2)h^2 - (1/2)h\\[/tex]

[tex]A(h) = (3/2)h^2 - (1/2)h[/tex]

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Answer:

you could do 2 students in each group with one group of 3

Step-by-step explanation:

sorry if i didn't answer correctly

Given that 60% of Olivia's fruit salad is made up of apples as opposed to Amadou's fruit salad's 52.63%, Olivia's fruit salad will have a more apple-forward flavor based on percent.

The amount of apples in each fruit salad needs to be compared in order to determine which salad will taste more apple-like.

There are 19 cups of fruit in Amadou's fruit salad, of which 10 cups are apples. By dividing the total number of cups of fruit by the number of cups of apples, and multiplying the result by 100, we can get the proportion of apples in Amadou's salad:

Apple's percent of Amadou's fruit salad is equal to (10/19) x 100, or 52.63%.

There are 5 cups of fruit in Olivia's fruit salad, of which 3 cups are apples. We can use the same formula to determine how much apple is in Olivia's salad:

Olivia's fruit salad contains 60% apples, or (3/5) x 100.

As a result, Olivia's fruit salad will taste more apple-like because apples make up 60% of it as opposed to only 52.63% of Amadou's fruit salad.

It is important to keep in mind that the maturity, sweetness, and freshness of the fruits used, as well as other elements like the dressing and presentation, may all affect how the fruit salad tastes.

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Answer:

Let's start by using the formula for finding the percentage: percentage = (part/whole) x 100 In this case, we know the percentage (2%) and the part (88 problems), but we don't know the whole (total number of problems on the test). So we can write: 2% = (88/whole) x 100 Simplifying, we get: 0.02 = 88/whole Multiplying both sides by the whole, we get: whole x 0.02 = 88 Dividing both sides by 0.02, we get: whole = 4400 Therefore, there were 4400 problems on the English test.

Answer:90 problems

Step-by-step explanation:

To solve the problem, we can use the formula:% correct = (number of correct answers / total number of questions) * 100%Since the student received a grade of 2%, we can write:2% = (number of correct answers / total number of questions) * 100%Simplifying this equation, we get:total number of questions = number of correct answers / 0.02We know that the student missed 88 problems, so the number of correct answers is:number of correct answers = total number of questions - 88Substituting this into the equation above, we get:total number of questions = (total number of questions - 88) / 0.02Simplifying this equation, we get:total number of questions = 50 * (total number of questions - 88)Solving for the total number of questions, we get:total number of questions = 90Therefore, there were 90 problems on the English test

The estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 0.825

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

To estimate the probability that it takes 10 or fewer shots to get his first successful shot, we need to add up the number of dots for the first 10 bars on the dot plot.

From the given dot plot, we can see that the number of dots for each value up to 10 shots are:

0 + 9 + 6 + 5 + 4 + 4 + 2 + 2 + 0 + 1 = 33

Therefore, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 33/40

This can also be written as a decimal:

P(10 or fewer shots) ≈ 0.825

Hence, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 0.825

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Option c y=0.48x+11 is the line of best fit to approximate the data in the scatterplot.

A statistical metric called a correlation coefficient shows the degree and direction of the association between two variables. Its value falls between -1 and 1, with -1 being a perfect negative correlation, 0 denoting no connection, and 1 denoting a perfect positive correlation. If there is a positive correlation, it implies that as one variable rises, the other variable likewise tends to rise, and if there is a negative correlation, it means that as one variable rises, the other variable tends to fall. The letter r is frequently used to represent the correlation coefficient.

Comparing the scatter plot with the given equations we observe that the slope of option b and d are very large as compared to the given distribution.

Observing from the given graph, the y-intercept of the best fit line will be nearly less than 20.

Thus, option c y=0.48x+11 is the line of best fit to approximate the data in the scatterplot.

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a) The association test, in this case, is a chi-square test of independence,

b) The conditions for the chi-square inference procedure are:

Independence

Sample size

c) In this case, the degrees of freedom are (3-1) x (4-1) = 6.

d) The researchers can generalize their results to the population of male students in the region from which the sample was drawn.

What is the association test?

An association test is a statistical test used to determine whether there is a relationship or association between two or more variables. The type of association test used depends on the nature of the variables being examined.

a) The association test, in this case, is a chi-square test of independence, which is used to determine whether there is a significant association between two categorical variables.

b) The conditions for the chi-square inference procedure are:

Independence: The sample is a simple random sample, so independence is satisfied.

Sample size: The expected count for each cell should be at least 5, which is satisfied for all cells in the table.

c) The degrees of freedom for the chi-square test are (r - 1) x (c - 1), where r is the number of rows and c is the number of columns in the table.

In this case, the degrees of freedom are (3-1) x (4-1) = 6. The p-value associated with a chi-square test statistic of 18.930 and 6 degrees of freedom is less than 0.01.

d) The researchers can generalize their results to the population of male students in the region from which the sample was drawn.

However, it may not be appropriate to generalize to other populations without further research to ensure the characteristics of the population are similar to those of the sample.

Hence,  a) The association test, in this case, is a chi-square test of independence,

b) The conditions for the chi-square inference procedure are:

Independence

Sample size

c) In this case, the degrees of freedom are (3-1) x (4-1) = 6.

d) The researchers can generalize their results to the population of male students in the region from which the sample was drawn.

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Answer:

Step-by-step explanation:

According to the given situation,

the area of figure A= l*b

                                =4m * 5m

                                =20m²

As the measures of the figure A and B is same,

the area of figure B = the area of figure A=20m²

the length of the side C and D are = 16m-8m-4m=4m

the area of figure C = l * b

                                 =4m*5m

                                 =20m²

As the measures of the figure C and D is same,

the area of figure D = the area of figure C=20m²

Area of the figure E=l * b

                               =8m * 13m

                               =104m²

∴ the area of the shaded region is =184m²

Answer:

sp= 8000.00.

loss percent= 20%

loss amount = 20% of sp

= 20÷100 × 8000

= 1600

now,

costprice = sp + loss amount

= 8000 + 1600

= 9600

Explanation:

Assuming the two religions are mutually exclusive, this would mean 80%+2% = 82% of people are either Hindu or Muslim (but not both).

The remaining 100% - 82% = 18% of people are neither religion mentioned.

x = number of people in the village

18% of x = 36

0.18x = 36

x = 36/0.18

x = 3600/18

x = 200

Then,

80% of x = 0.80*x = 0.80*200 = 160 people are Hindu

The Venn diagram is shown below.

The volume of the apple is approximately 832.2 cubic centimeters.

The following equation determines a sphere's volume:

V = (4/3)πr³

When V denotes the sphere's volume, r denotes its radius, and denotes the mathematical constant pi (approximately 3.14). By seeing the sphere as an unlimited number of little cylinders piled on top of one another, the formula may be created. Each cylinder has a height equal to the sphere's shell thickness and a radius equal to the sphere's radius.

The volume of a sphere:

V = (4/3)πr³

Here, r = d/2 = 11.9 cm / 2 = 5.95 cm

Substituting the values we have:

V = (4/3)π(5.95 cm)³ ≈ 832.2 cm³

Therefore, the volume of the apple is approximately 832.2 cubic centimeters.

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The answer to the given question about inscribed angles intercepting an arc is option A. 100

As we know that the measure of an inscribed angle is half the measure of the intercepted arc, we can use the formula:

Measure of inscribed angle = 1/2 × Measure of intercepted arc

So, if the intercepted arc has a measure of 200 degrees, then the measure of the inscribed angle is:

Measure of inscribed angle = 1/2 × 200 degrees

= 100 degrees

Therefore, the answer is A. 100 degrees. In a circle, an inscribed angle is an angle formed by two chords of the circle that have a common endpoint on the circle. The measure of an inscribed angle is half the measure of the intercepted arc. Therefore, if an arc has a measure of 200, then an inscribed angle that intercepts that arc will have a measure of half of 200, which is 100 degrees.

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