The table below shows the number of tickets sold, t, at a high school basketball game, and the amount of money collected, m.

Tickets Sold (t) Money Collected (m)
25 $62.50
35 $87.50
40 $100

Which equation will calculate the amount of money collected after t tickets are sold?

It was 2 hours

A bicyclist ride 3 mph (miles per hour) to cover 12 miles in 4 hours

The distance of the first ride, ridden for 120 minutes at 18 mph, was 36 miles. To cover 12 miles in 4 hours, the bicyclist must ride at a speed of 3 mph.

To find the distance of the first ride, we can use the formula:

Distance = Speed × Time

Given that the bicyclist rides for 120 minutes (2 hours) at an average speed of 18 miles per hour:

Distance = 18 miles/hour × 2 hours = 36 miles

So, the distance of the first ride was 36 miles.

To find the speed the bicyclist must ride to cover 12 miles in 4 hours, we use the same formula:

Speed = Distance / Time

Given that the distance is 12 miles and the time is 4 hours:

Speed = 12 miles / 4 hours = 3 miles per hour

The bicyclist must ride at a speed of 3 miles per hour to cover 12 miles in 4 hours.

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Answer:

The money was invested for 16 years

Step-by-step explanation:

This is a compound interest problem and the following information has been provided;

Principal, P = 2500

Rate, r = 0.05 compounded semiannually. This will imply an effective rate of 0.05/2 = 0.025 effective per semiannual period.

Accumulated amount, A = 5509.39

We are required to determine the duration of investment in years. We let the number of years be n. We then use the compound interest formula;

[tex]A=P(1+r)^{n}\\\\5509.39=2500(1+0.025)^{2n}[/tex]

We raise to power 2n since there are 2n semiannual periods in n years. The next step is to divide both sides by 2500;

[tex]2.203756=1.025^{2n}\\[/tex]

We introduce logs in order to solve for n;

[tex]ln(2.203756)=2nln(1.025)\\\\2n=\frac{ln(2.203756)}{ln(1.025)}\\ \\2n=32\\\\n=16[/tex]

Answer:

This is a graph of y = -x,

slope of graph = -1,

Y-intercept = 0

This line passes through the origin, so its equation follows the form

[tex]y=mx[/tex]

The slope [tex]m[/tex] can be computed using the "rise over run" technique: each time you increase x by 1, y decreases by 2. So, the slope is -2.

The equation is thus

[tex]y=-2x[/tex]

Answer:

Check attached graph

Step-by-step explanation:

Given inequality is [tex]-2a-5>3[/tex].

Now we need to graph the given inequality to find the correct choice.

[tex]-2a-5>3[/tex]

[tex]-2a-5+5>3+5[/tex]

[tex]-2a>8[/tex]

[tex]-\frac{2a}{-2}<\frac{8}{-2}[/tex]

[tex]a<-4[/tex]

that means line will go on the left side of -4.

since we have <, so there will be an open circle at -4.

Hence final graph of the given problem looks like:

Answer:

C. 3Pi/2 or 270 degrees

Step-by-step explanation:

The first step is to ignore the negative sign and then evaluate the arcsin of 1 to obtain the reference angle of θ in the first quadrant;

θ = arcsin(1)

θ = 90 degrees or equivalently pi/2

Since the sine of θ was given as -1, this will imply that θ lies either in the third or forth quadrant where the sine of an angle is negative.

To obtain the value of θ in the third quadrant we simply add 180 degrees of pi radians to our reference angle;

90 + 180 = 270 degrees

pi/2 + pi = 3/2 pi

Answer:

4.5

Step-by-step explanation:

because 2 3 4 4 5 7 9 11

4.5 is the middle number, between 4 and 5 since you find what the middle number is

Here is some fun:

[tex]mean=\frac{\Sigma_{0}^{n}a_r}{n}=\frac{a_0+a_1+\dots+a_{\infty}}{\infty}[/tex]

[tex]

mean=\frac{4+5+9+2+7+4+3+11}{8}=\frac{45}{8}=\boxed{5.625}

[/tex]

And now the real work:

[tex]median=\frac{2+7}{2}=\boxed{4.5}[/tex]

The answer is B. 4,5

Hope this helps.

r3t40

Answer:

Option B

Step-by-step explanation:

we know that

A line perpendicular to the x-axis is a line parallel to the y-axis

so

the equation of the line is of the form x=(+/-)a

The slope of the line is undefined

where

a is a real number

therefore

x=6 is a line perpendicular to the x-axis

Answer:

B. [tex]x = 6[/tex]

Step-by-step explanation:

The x-axis is the line of [tex]0 = y[/tex] [horizontal line], therefore the ONLY live perpendicular to that would be [tex]x = 6[/tex], which is a vertical line, giving you a right angle in the centre.

I am joyous to assist you anytime.

Answer:

[tex]\boxed{\text{a. 111.1 m; b. 56 575 m}^{3}}[/tex]

Step-by-step explanation:

a. Height

(i) Height of prism

The height of the prism is 70 m.

(ii) Height of pyramid

Consider the red triangle in the diagram.

The diagonal of the square base is given by

d² = a² + a² = 2a²

d² = 2(26)² = 2 ×676 = 1352 m²

d = √1352 = 36.77 m

The base of the triangle R is

R = ½d = ½ × 36.77 = 18.38 m

Now,

h² + R² = e²

h² + 18.38² = 45²

h² + 338  = 2025  

h² = 1687

h = 41.07 m

(iii) Total height

Total height = height of prism + height of pyramid = 70 + 41.07 = 111.1 m

b. Volume

(i) Volume of prism

V = lwh

V = 70 × 26 × 26 = 47 320 m³

(ii) Volume of pyramid

The formula for the volume of a square pyramid is  

V = ⅓a²h

V = ⅓ × 26² × 41.07 = 9255 m³

(iii) Total volume

Total volume = volume of prism + volume of pyramid

V = 47320 + 9255 = 56 575 m³

The total height of the building is [tex]\boxed{\textbf{111.1 m}}[/tex]

The total volume of the building is [tex]\boxed{\textbf{56 575 m}^{3}}[/tex]

To make generalizations from sales data of the Random stationery employees or car salespersons, statistical analysis using histograms, frequency polygons, time series graphs, and box plots is necessary to visually interpret the distribution and variance within the data.

Understanding Sales Data and Statistical Representation

When reviewing the sales data of Random Stationary's employees or the weekly sales of car salespersons, we are engaging in the statistical analysis of a chosen sample. Here, histograms, frequency polygons, time series graphs, and box plots are used to graphically represent data obtained from these samples. These visual tools allow us to interpret data distributions and make generalizations about the overall population from which the sample was taken.

Examples of Data Representation

In the provided example regarding the number of cars sold by 65 randomly selected salespersons, data is summarized in a frequency table. This leads to the construction of a histogram or a box plot where the central tendency and the dispersion of data can be observed. Similarly, in a workplace setting like that of Yoonie’s personnel reviews, the central limit theorem suggests that sampling distributions approach a normal distribution as sample size increases. This is especially true when concluding population averages from sample means.

Making Generalizations from Samples

When looking at the data from Random Stationary’s employees or any other such gathered data, mean, median, mode, range, and standard deviation can provide insights into sales performance. By examining the data visually through box plots, one can comment on the spread and concentration of data, which indicates whether sales performance is consistent or variable across shifts or individuals. Random sampling methods, systematic sampling, and stratified sampling all contribute to acquiring data that can help make valid generalizations when applied correctly.

Morning shift workers generally have lower sales (mean: 32, median: 36, mode: 20) compared to afternoon shift workers (mean: 46, median: 33, mode: 31), with afternoon workers showing a wider range (18).

To make generalizations based on the provided statistical information, let's break down each measure of central tendency and spread for both morning shift workers and afternoon shift workers.

1. **Mean**: The mean is the average value of a set of numbers. It is calculated by adding up all the numbers and then dividing by the total count.

  - For morning shift workers: Mean = (Sum of sales for morning shift workers) / 12 = 32

  - For afternoon shift workers: Mean = (Sum of sales for afternoon shift workers) / 12 = 46

2. **Median**: The median is the middle value in a set of numbers when they are arranged in ascending order. If there is an even number of values, the median is the average of the two middle values.

  - For morning shift workers: Median = 36

  - For afternoon shift workers: Median = 33

3. **Mode**: The mode is the value that appears most frequently in a set of numbers.

  - For morning shift workers: Mode = 20

  - For afternoon shift workers: Mode = 31

4. **Range**: The range is the difference between the largest and smallest values in a dataset.

  - For morning shift workers: Range = Largest value - Smallest value = B - I (not provided)

  - For afternoon shift workers: Range = 62 - 44 = 18

Answer:

Option B.

Step-by-step explanation:

The constant of proportionality is the constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality.

Given that the graph is a straight line, we can find the constant of proporctionality just by selecting a point, and then dividing the y-value by the x-value.

We can see from the graph that when y=5, x=4. Then, the constant of proportionality comes to be:

k = 5/4 = 1.25.

Then, the correct option is Option B.

Answer:

n = 4

Step-by-step explanation:

Given

10n + 2 = 7n + 14

Collect terms in n on the left side and numbers on the right side

Subtract 7n from both sides

3n + 2 = 14 ( subtract 2 from both sides )

3n = 12 ( divide both sides by 3 )

n = 4

Answer n=4

Step-by-step explanation: Collect the like terms 10n-7n=14-2

3n=12 divide both sides by 3

5 ÷ 2 * 7 + 5/7

Simplify 2 * 7 to 14

5 ÷ 14 + 5/7

Simplify 14 + 5 to 19

5 ÷ 19/7

Use this rule: a ÷ b/c = a * c/b

5 * 7/19

Simplify

35/19

Convert to a mixed fraction

= 1 16/19

Answer:

[tex]\large\boxed{1\dfrac{16}{19}}[/tex]

Step-by-step explanation:

[tex]5\div2\dfrac{5}{7}\qquad\text{convert the mixed number to improper fraction}\\\\2\dfrac{5}{7}=\dfrac{2\cdot7+5}{7}=\dfrac{19}{7}\\\\=5\div\dfrac{19}{7}=5\cdot\dfrac{7}{19}=\dfrac{(5)(7)}{19}=\dfrac{35}{19}=1\dfrac{16}{19}[/tex]

Answer:

120°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 6, hence

sum = 180° × 4 = 720°, thus

angle measure = 720° ÷ 6 = 120°

Answer:

38

Step-by-step explanation:

0.17 is about 0.2, and 193 is about 190.

0.2 * 190 = 38.

So 0.17 * 193 is about 38

32.81 is your answer

z÷x

-6÷3

=-2

Answer is -2

Answer:

(-6)/3 = -2

Step-by-step explanation:

you have to change the variables with the numbers

Answer:

y= 2/3 x

Step-by-step explanation:

First plot the points on a Cartesian plan

You will notice a straight line passing through the origin (0,0)

Find the gradient of the line;

m=change in y/change in x

m=2-0/3-0 =2/3

Find the equation of the line

y-2/x-3 =2/3

3(y-2) = 2(x-3)

3y-6= 2x-6

3y=2x-6+6

3y=2x

y=2/3 x + 0

Answer:

47

Step-by-step explanation:

www.alcula.com/calculators/statistics/median/

Each of these numbers represents the weight of a student in kilograms. Hence, the median of the given data set is 47.

Median is such a number for the arranged data set(ascending or descending order) such that to its left and to its right belong the same number of observations.

Each of these numbers represents the weight of a student in kilograms.

39, 48, 45, 48, 51, 46, 52, 51, 43, 41

We need to find the median of this data set.

In order to find the median, arrange the data in ascending order.

39, 41, 43, 45, 46, 48, 48, 51, 51,  52,

[tex]M= \dfrac{46 + 48 }{2} \\\\M = \dfrac{94}{2} \\\\M= 47[/tex]

Hence, the median of the given data set is 47.

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Let S = the amount of sales.

She earns 4% of her sales, this would be written as 0.4S ( you multiply the percent as a decimal by the amount of sales).

You then need to add that amount to her salary so you now have 0.4s + 2100

She wants to earn at least 2900 so the inequality becomes:

2900 ≥ 0.4s + 2100

Her sales would need to be:

800 ≥0.4s

s≥ 800/0.4

s ≥ 2000

Answer:

Choice B: BD/DA = CE/EA

Step-by-step explanation:

Slope is rise over run. For the two slopes to be equal, the rise over run of the two triangles must be equal.

The rise over run for triangle ABD is BD/DA.

The rise over run of triangle ACE is CE/EA.

For the slopes to be equal, BD/DA = CE/EA

Answer: Choice B.

Answer:

The third alternative is correct

Step-by-step explanation:

In hypothesis testing, the null hypothesis H0 is the hypothesis of no difference and as such it always contains an equality sign. The equality sign could be either of the following alternatives;

=, equal to

≤, less than or equal to

≥, greater than or equal to

In the question presented the claim is that students who practice taking all of their regular tests on the computer will do better on the state's final exam than the students taking their regular tests by paper and pencil.  

This implies that the average on the state exam of students using paper and pencil tests is less than the average of the students using computer tests. Since the null hypothesis must contain an equality sign, the third alternative becomes our null hypothesis, H0.

The car will travel 800 kilometers in 5 hours.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given

1 mile = 1.6 km

100 mile = 1.6 * 100 = 160 km

in 1 hr car travels 160 km

in 5 hrs car travels = 160 * 5 = 800 km

The car will travel 800 kilometers in 5 hours.

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In 5 hours, the car will travel 800 kilometers.

To convert the car's speed from miles per hour to kilometers per hour, you multiply by the conversion factor of 1.6 kilometers per 1 mile. Therefore, a speed of 100 miles per hour is equivalent to 100 × 1.6 = 160 kilometers per hour.

Next, to calculate how many kilometers the car will travel in 5 hours at the speed of 160 kilometers per hour, you simply multiply the speed by the time. The car will travel 160 km/h × 5 h = 800 kilometers in 5 hours.

Step-by-step explanation:

Mean is the average and that means you add up all the numbers and divide it by its amount.

Interquartile Range is the range of Quartile 3 minus Quartile 1

Range is the highest number minus the lowest number

mean the sum of a set of data divided by the number of items in the set

range the difference between the largest and smallest data points

interquartile range  the difference between the upper quartile and the lower quartile

Answer:

Step-by-step explanation:

First step:

Calculate the hypotenuse of a right triangle.

Use the Pythagorean theorem:

[tex]h^2=3^2+4^2\\\\h^2=9+16\\\\h^2=25\to h=\sqrt{25}\\\\h=5\ cm[/tex]

Second step:

We have

two right triangles with legs a = 3cm and b = 4 cm

one rectangle 4cm × 2cm

one rectangle 3cm × 2cm

one rectangle 5cm × 2cm

Calculate each area:

The formula of an area of a right triangle:

[tex]A=\dfrac{ab}{2}[/tex]

Substitute:

[tex]A_1=\dfrac{(3)(4)}{2}=(3)(2)=6\ cm^2[/tex]

The formula of an area of a rectangle l × w:

[tex]A=lw[/tex]

Substitute:

[tex]A_2=(4)(2)=8\ cm^2\\\\A_3=(3)(2)=6\ cm^2\\\\A_4=(5)(2)=10\ cm^2[/tex]

Third step:

Calculate the Surface Area of the figure:

[tex]S.A.=2A_1+A_2+A_3+A_4[/tex]

Substitute:

[tex]S.A.=2(6)+8+6+10=36\ cm^2[/tex]

Answer:

the correct answer is between a and b. So I think the answer is b

Answer:

The answer is B.

Step-by-step explanation:

(5)[tex]\frac{3}{4}[/tex]+[tex]\frac{1}{5}[/tex](4)

[tex]\frac{15}{20}[/tex]+[tex]\frac{4}{20}[/tex]=[tex]\frac{19}{20}[/tex]

The first step is to multiply the left side by 5 and the right side by 4 because you want the denominator to be the same. Then you add [tex]\frac{15}{20}[/tex]+[tex]\frac{4}{20}[/tex] to get [tex]\frac{19}{20}[/tex]:)

Answer:

p = - 6, p = - 2

Step-by-step explanation:

Given

- 2p² = 16p + 24

Subtract 16p + 24 from both sides

- 2p² - 16p - 24 = 0 ← in standard form ( divide all terms by - 2)

p² + 8p + 12 = 0

To factor the quadratic

Consider the factors of the constant term (+ 12) which sum to give the coefficient of the p- term (+ 8)

The factors are + 6 and + 2, since

6 × 2 = 12 and 6 + 2 = 8, thus

(p + 6)(p + 2) = 0

Equate each factor to zero and solve for p

p + 6 = 0 ⇒ p = - 6

p + 2 = 0 ⇒ p = - 2

Answer:

42 units^2.

Step-by-step explanation:

We are given that it is a rectangle so its area is the product of the length of adjacent sides.

Length  of the horizontal line = 11 - 4 = 7 units ( from the first 2 points) and  the length of an adjacent side is 9 - 3 = 6 units (from the second and third points).

Area = 7 * 6 = 42.

Answer:

area of rectangle = 42

Step-by-step explanation:

area of rectangle = length × width

                             = 7 × 6

                             = 42

Answer:

well a perfect square of trinomial if it can be factored into a binomial multiplied to itself. so theres step by step to

Step-by-step explanation:

For example, in the trinomial x2 - 12x + 36, both x2 and 36 are perfect squares.welcome

Answer is provided in the image attached.

For this case we have that by definition, the formula to count the total number of different permutations is:

[tex]nP_ {r} = \frac {n!} {(n-r)!}[/tex]

SUstituyendo:

[tex]n = 8\\r = 5[/tex]

We have:

[tex]8P_ {5} = \frac {8!} {(8-5)!} = \frac {8!} {3!} = \frac {8 * 7 * 6 * 5 * 4 * 3!} {3! } = 6720[/tex]

ANswer:

[tex]8P_ {5} = 6720[/tex]

Answer:

20% it would be 10% if there was 10 items. 5 items mean every item has 20%.

Step-by-step explanation:

Answer:  0.20

Step-by-step explanation:

Given : The number of side dishes for the lunch menu =6

The number of ways to select 3 dishes from 6 :

Total outcomes : [tex]^6C_3=\dfrac{6!}{3!(6-3!)} \ \ [\because\ ^nC_r=\dfrac{n!}{r!(n-r)!}\ ][/tex]                  

If applesauce and broccoli is already selected , then we need to select only one dish out of remaining 4 dishes.

Number of ways to select 1 dish from 4 :

Favorable outcomes: [tex]^4C_1=\dfrac{4!}{1!(4-1)!)}=4[/tex]

Now, the theoretical probability that applesauce and broccoli will both be offered on Monday :-

[tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{4}{20}=0.20[/tex]

Hence, the theoretical probability that applesauce and broccoli will both be offered on Monday = 0.20

Answer: C.

Step-by-step explanation:

Diameter = Radius/2

So, the radius would be 6.5 in.

The formula for the volume of a sphere is: V = 4/3 (3.14) r^3.

So, once you "plug in" the radius, you get an equation of V = 4/3 (3.14) r^3.

And, once you solve the equation, you get and answer of 1,150 in.^3, rounded to the nearest cubic inch.

The volume of a sphere with a diameter of 13 inches, using the formula V = 4/3 * π * r³ and rounding off to the nearest cubic inch, is approximately 1151 cubic inches or choice C, 1150 in³.

To find the volume of a sphere, you can use the formula V = 4/3 * π * r³, where V is the volume and r is the radius. In this case, the diameter of the sphere is given as 13 inches. So, the radius would be half the diameter, which is 6.5 inches.

Plugging the values into the formula, we get V = 4/3 * 3.14 * (6.5)³. Calculating this gives an approximate value of 1151 cubic inches. Since we need to round to the nearest cubic inch, the final volume is 1151 in³.

So, the correct choice is C. 1150 in³.

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