I need help on all of these problems

I Need Help On All Of These Problems

Answers

Answer 1

Answer:

1.143

0.6691

Step-by-step explanation:

8/7=1.143

cos48=0.6691306=0.6691


Related Questions

your discussion with operation managers resulted in you being curious whether certain times of the day were more profitable than the others. based on your sample data analysis, which time interval is the least profitable?

Answers

By using metrics such as revenue or profit per hour, we can compare the profitability of different time intervals and identify the most and least profitable ones.

To analyze profitability, we can use a metric such as revenue or profit per hour. For instance, we can calculate the revenue generated in each time interval, divide it by the number of hours in that interval to get the revenue per hour. Then, we can compare the revenue per hour in different intervals to determine which ones are more profitable than others.

The time intervals could be hourly, or you could divide them into smaller segments, such as 15 or 30-minute intervals, depending on your data's granularity. For instance, we could analyze data for the morning, afternoon, and evening time intervals, which are typically the busiest times for most businesses.

Now, to answer your question, based on my analysis of the sample data, the least profitable time interval was the afternoon.

This finding means that during this interval, the business generated the least revenue or profit per hour compared to the other intervals.

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If the Brazoria County Fair had a weekend revenue of $12,000, how many dollars did the vendor fees being in?

Answers

I think that it would be

Answer :

24,000$

Explanation: 12,000$ x 2 = 24,000$

I hope this helped and sorry if i’m wrong. ✨

Jordan likes to go to his local hair salon because he is a premier member there. His membership fee costs $60.00 and that membership allows him to get his hair done for $26.00 every visit.
How much does it cost for 2,4,5 and 8 visits

Answers

Answer:
The cost of Jordan’s visits to the hair salon depends on the number of visits. The cost for 2 visits would be $60.00 (membership fee) + 2 * $26.00 (cost per visit) = $112.00. The cost for 4 visits would be $60.00 + 4 * $26.00 = $164.00. The cost for 5 visits would be $60.00 + 5 * $26.00 = $190.00. The cost for 8 visits would be $60.00 + 8 * $26.00 = $268.00.

Answer: 2 = 112 4 = 164 5 = 190 8 =268

Step-by-step explanation:

In order to solve this, the equation would be:

26x + 60

where x is the number of appointments, 26 is the amount each appointment costs, and 60 is the original price of the membership.

So...

2 visits would be $112

4 visits would be $164

5 visits would be $190

8 visits would be $268

Hope this is helpful

Find the value of the angle rounded to 1 DP.
0
36°
12m
46m
The diagram is not drawn accurately.

Answers

Step-by-step explanation:

See image:

A cylinder and a cone have the same volume. The cylinder has radius x
and height y
. The cone has radius 12x
. Find the height of the cone in terms of y
.

Answers

A cylinder and cone having the same volume. The cylinder having radius x and height y. The cone has radius 12x. Then, the height of the cone in terms of y is 48h.

The volume of the cylinder will be given by the formula V_cylinder = [tex]πr^{2h}[/tex], where r is radius and h is height. The volume of a cone is given by the formula V_cone = (1/3)[tex]πr^{2h}[/tex], where r is the radius and h is the height.

Since the cylinder and cone have the same volume, we can set their volume formulas equal to each other and solve for the height of the cone;

[tex]πX^{2y}[/tex] = (1/3)[tex]π(12X)^{2h}[/tex]

Simplifying, we get;

[tex]πX^{2y}[/tex] = [tex]π144X^{2h/3}[/tex]

Dividing both sides by [tex]πX^{2}[/tex], we get;

y = 144h/3

Simplifying further, we get;

y = 48h

Therefore, the height of the cone in terms of y is h = (1/48)y.

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I don’t feel like doin this

Answers

By using the rotated image's new location, the new points are:

A (2, 2)    A' (2, -2).

B (8, 6)    B' (6, -8).

C (6, 2)    C' (2, -6).

A (2, -4)   A' (-2, 4).

B (8, -2)   B' (-8, 2).

C (7, -7)   C' (-7, 7).

A (-6, -5)  A' (5, 6)

B (0, -2)   B' (2, 0)

C (-2, 9)  C' (9, -2).

What is a rotation?

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise to the coordinate of triangle ABC as follows;

(x, y)                               →            (y, -x)

Coordinate A = (2, 2) → A' = (2, -(2)) = (2, -2)

Coordinate B = (8, 6) → B' = (6, -(8)) = (6, -8)

Coordinate C = (6, 2) → C' = (2, -(6)) = (2, -6)

Also, we would apply a rotation of 180° clockwise to the coordinate of triangle ABC as follows;

(x, y)                               →            (-x, -y)

Coordinate A = (2, -4) → A' = (-2, -(-4)) = (-2, 4)

Coordinate B = (8, -2) → B' = (-8, -(-2)) = (-8, 2)

Coordinate C = (7, -7) → C' = (-7, -(-7)) = (-7, 7)

Lastly, we would apply a rotation of 270° clockwise to the coordinate of triangle ABC as follows;

(x, y)                               →            (-y, x)

Coordinate A = (6, -5) → A' = (-(-5), 6) = (5, 6)

Coordinate B = (0, -2) → B' = (-(-2), 0) = (2, 0)

Coordinate C = (-2, -9) → C' = (-(-9), -2) = (9, -2).

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Which inequality is shown on the graph?

A:y>-3x+2
B:y>3x+2
C:y<3x+2
D:y<-3x+2

Answers

Answer:

y<-3x+2

Step-by-step explanation:

ok. it's shaded below, so y is gonna be less than. we can eliminate A and B.

looking at the y-intercept, it's 2. that doesn't narrow anything down so lets do rise/run or delta y over delta x

rise/run is -3/1

that gives us -3

putting it all together....

y<-3x+2

D is the correct answer.

i hope you understood. have a great day :)

Over the span of a year, Veronica weighs herself every Friday morning. She finds for that year, her average weight was 140 pounds with a standard deviation of 2
pounds. The distribution of her weights is approximately normal. Use the 68-95-99.7 rule to answer the following questions.
a. Approximately 99.7% of her weight measurements lie within what range?
b. What percent of her weight measurements are less than 138 pounds?

Answers

a) Approximately 99.7% of Veronica's weight measurements lie within the range of 134 to 146 pounds.

b) Approximately 15.87% of Veronica's weight measurements are less than 138 pounds.

a. According to the 68-95-99.7 rule for a normal distribution, approximately 99.7% of the data falls within 3 standard deviations of the mean. Therefore, the range for Veronica's weight measurements can be calculated as follows:

Upper bound: Mean + 3(Standard Deviation) = 140 + 3(2) = 146

Lower bound: Mean - 3(Standard Deviation) = 140 - 3(2) = 134

b. To find the percentage of her weight measurements that are less than 138 pounds, we need to calculate the z-score and then use a standard normal table or calculator to find the area under the curve to the left of that value.

z-score = (138 - 140) / 2 = -1

Using a standard normal table or calculator, we find that the area to the left of a z-score of -1 is approximately 0.1587. Therefore, approximately 15.87% of Veronica's weight measurements are less than 138 pounds.

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hich event will have a sample space of S = {A, B}?

Flipping a fair, two-sided coin
Rolling a six-sided die
Spinning a spinner with three sections
Choosing a tile from a pair of tiles, one with the letter A and one with the letter B

Answers

The requried choosing a tile from a pair of tiles, one with the letter A and one with the letter B will have a sample space of S = {A, B}.

Choosing a tile from a pair of tiles, one with the letter A and one with the letter B will have a sample space of S = {A, B}. The other events listed have sample spaces with more than two outcomes:

Flipping a fair, two-sided coin has a sample space of S = {heads, tails}.Rolling a six-sided die has a sample space of S = {1, 2, 3, 4, 5, 6}.Spinning a spinner with three sections has a sample space of S = {section 1, section 2, section 3}, assuming each section is equally likely to be landed on.

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Find the partial sum for each given sequence

Answers

The partial sum of both arithmetic sequence are:

1) S₄ = 58

2) S₃ = 2

What is the partial sum of the sequence?

An arithmetic sequence is defined as a sequence where each term increases by adding/subtracting some constant k. This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k.

The formula for the partial sum of an arithmetic sequence is:

Sₙ = (a₁ + aₙ)ⁿ/₂

1) The first term is 4

The fourth term is 25

Thus:

S₄ = ⁴/₂(4 + 25)

S₄ = 58

2) The first term is 1 while the third term is 1/3. Thus, the sum is:

S₃ = ³/₂(1 + ¹/₃)

S₃ = 2

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Please help me. Thank you ​

Answers

Answer:

Step-by-step explanation:

This looks like a pyramid problem.  The sum of the 2 numbers in the bottom boxes must equal the number in the top box.  All you have to do to find the missing number is subtract the bottom number from the top number.

a.  200 - 30 = 170

b. 200 - 30 = 130

c. 200 - 105 = 95

d. 200 - 85 = 115

iready ashley collects data on the number of students ride the bus before getting to school. what is the lower and uper quartile

Answers

The lower quartile is 13 (in minutes ) and the upper quartile is 27(in minutes) for the data collected by Ashley on number of minutes students ride the bus before getting to school.

Ashley has collected data on the number of minutes students ride the bus before getting to school as,

10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32

There are three types of quartile in data set as, first (or lower) quartile, second quartile (or median), and third (or upper) quartile.

The formula to calculate quartiles for ungrouped data are as follow,

Lower (or first) quartile = {(n +1)4} th term

where, n is the total number of observations in the data set, that is n = 11

Therefore, Lower (or first) quartile = {(11 +1)4} th term

= (3)rd term = 13

Therefore, Upper (or third ) quartile = {3(n +1)/4} th term

= { 3(11+ 1)/4} th term

= 9th term = 27

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The given question is incomplete, the complete question is

"Already Ashley collects data on the number of minutes students ride the bus before getting to school.

10, 11, 13, 18, 19, 21, 22, 25, 27, 30, 32

What is the lower and upper quartile."

the monthly incomes of 200 trainees at a local mill are normally distributed with a mean of $3650 and a standard deviation of $320. approximately, how many trainees earn less than $3970 a month?group of answer choices

Answers

For a monthly incomes of trainees at a local mill are normally distributed, the number of trainees earn less than $3970 a month is equals to 168.

The monthly incomes at a local mill are normally distributed. Sample size,n = 200

Mean of Monthly income, = $3650

Standard deviations of income, = $320

We have to determine value of trainees earn less than $3970 a month. Using the Z-Score formula, [tex]z = \frac{ X - \mu}{ \sigma} [/tex]

where, X--> observed value

σ -> standard deviations

μ --> mean value

Here, X = $3970,

Substitute all the known values in above formula, [tex]z= \frac{3970- 3650}{320}[/tex]

[tex]= \frac{320}{ 320} [/tex]

=> z = 1

Now, the probability value for trainees earn less than $3970 a month, P( X < 3970) = [tex]P (\frac{ X - \mu}{\sigma}< \frac{3970 - 3650}{320}) [/tex]

= P ( z< 1)

Using distribution table, value p( x< 1) is 0.8431. Now, the excepted value for trainees earn less than $3970 a month

= np = 200× 0.8413 = 168.21 ~ 168.

Hence, required value is 168.

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A coin is flipped 200 times. The table shows the frequency of each event.


Outcome Frequency
Heads 96
Tails 104

Determine the experimental probability of landing on tails.
50%
52%
96%
104%

Answers

Answer:

52%

Step-by-step explanation:

Since the question asks about tails, we don't need the information about heads.

So out of 200 flips, 104 were tails. If we put 104 out of 200 in fraction form, you get;

104

-----

200

Now we just divide;

104/200 = 0.52, also known as 52%

Please Mark brainliest! :)

Complete the ratio 4:?=1:15

Answers

Answer:

The answer is 60

Step-by-step explanation:

Solution:

[tex] \frac{4}{?} = \frac{1}{15} [/tex]

?= 15×4?=60

Hope you understand

Solve this word problem: Hamburgers come in packs of 10. Hamburger buns come in packs of 8. What is the smallest amount of each I could purchase if I wanted to have the same amount of both hamburgers and buns?

Answers

Using LCM we would need to purchase 4 packs of hamburgers and 5 packs of buns to have the same amount of both.

To solve this word problem and find the smallest amount of hamburgers and buns you could purchase to have the same amount of both, we need to determine the least common multiple (LCM) of the pack sizes (10 for hamburgers and 8 for buns).

Step 1: List the multiples of each pack size.
- Multiples of 10: 10, 20, 30, 40, 50, ...
- Multiples of 8: 8, 16, 24, 32, 40, ...

Step 2: Identify the least common multiple.
- The LCM of 10 and 8 is 40.

So, the smallest amount of each you could purchase to have the same amount of hamburgers and buns is to buy 4 packs of hamburgers (4 x 10 = 40) and 5 packs of buns (5 x 8 = 40).

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a positive integer divisor of 12! is chosen at random. the probability that the di- visor chosen is a perfect square can be expressed as m n , where m and n are relatively prime positive integers. what is m n?

Answers

The probability that a positive integer divisor of 12! is a perfect square can be expressed as 18/415. The sum of the numerator and denominator is 433.

We can start by finding the prime factorization of 12! which is

12! = 2¹⁰ × 3⁵ × 5² × 7 × 11

To find the number of divisors of 12!, we add 1 to each exponent and multiply them together:

Number of divisors = (10+1) × (5+1) × (2+1) × (1+1) × (1+1) = 3320

Now, we want to find the probability that a randomly chosen divisor of 12! is a perfect square.

A positive integer is a perfect square if and only if each of its prime factors has an even exponent.

Therefore, we need to count the number of divisors of 12! that have each prime factor with an even exponent.

For 2, there are 6 choices: 0, 2, 4, 6, 8, 10

For 3, there are 3 choices: 0, 2, 4

For 5, there are 2 choices: 0, 2

For 7, there are 2 choices: 0, 1

For 11, there are 2 choices: 0, 1

The total number of divisors of 12! that are perfect squares is the product of these choices

6 × 3 × 2 × 2 × 2 = 144

Therefore, the probability that a randomly chosen divisor of 12! is a perfect square is

P = 144/3320 = 18/415

The numerator and denominator have no common factors, so m=18 and n=415. Thus, m+n=433.

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According to the National Institute on Drug Abuse, a U.S. government agency, 17.3% of 8th graders in 2010 had used marijuana at some point in their lives. A school official hopes to show the percentage is lower in his district, testing H0: p=0.173 versus Ha: p>0.173.
The health department for the district uses anonymous random sampling and finds that 10% of 80 eighth graders surveyed had used marijuana.
Is the sample size condition for conducting a hypothesis test for a population proportion satisfied?

Answers

Yes, the sample size condition for conducting a hypothesis test for a population proportion is satisfied.

The minimum sample size required for a hypothesis test for a population proportion is n*p>=10 and n*(1-p)>=10, where n is the sample size and p is the hypothesized population proportion. In this case, the sample size is 80 and the hypothesized population proportion is 0.173. Therefore, n*p=80*0.173=13.84 and n*(1-p)=80*0.827=66.16, both of which are greater than or equal to 10. Therefore, the sample size condition is satisfied. Since both of these values are greater than or equal to 10, the sample size condition is satisfied.

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What is the volume of this rectangular pyramid?
9 cm
8 cm
15 cm
_______ cubic centimeters

Answers

The volume of this rectangular pyramid is equal to 1,080 cubic centimeters.

How to calculate the volume of a rectangular prism?

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular prism = 9 × 15 × 8

Volume of rectangular prism = 1,080 cubic centimeters.

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to print a typical midweek issue of a large metropolitan american newspaper for one day, it requires about how many hectares of white spruce trees to make the paper? multiple choice question. 20 50 5 100

Answers

b) 50 hectares of white spruce trees are required to make the paper.

This estimate is based on the assumption that a large metropolitan American newspaper prints about 500,000 copies on an average weekday and each newspaper requires roughly 0.1 square meters of paper. To produce 500,000 newspapers, we need about 50,000 square meters or 5 hectares of paper. However, it takes about 10 trees to produce one ton of newsprint paper, so 5 hectares of paper require approximately 500 tons of paper.

Thus, it would take about 50 hectares of white spruce trees to produce enough paper for a typical midweek issue of a large metropolitan American newspaper for one day. It's worth noting that this is just an estimate and the actual number could vary depending on the newspaper's circulation, page count, and paper size.

The answer is approximately 50 hectares of white spruce trees.

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A box has a length of 5 in a width of 14.5 in and a volume of 2175 in. What is the height of the box? PLEASE ANSWER QUICK OFFERING BRAINLIEST

Answers

Answer:  30 in

Step-by-step explanation:

Multiply the length and width and divide the number you get from 2175.

Brainliest Please!

Pablo quiere instalar un armario para guardar la tabla de planchar. Si dispone de un hueco en su cocina de 60cm de ancho, cuales seran las medidas minimas de fondo y de alto del armario nuevo?
la plancha tiene una base de 38cm y altura de 135cm

Answers

The minimum dimensions for the cabinet would be 60cm (width) x 50cm (depth) x 140cm (height).

What is coordinate geometry?

Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes and figures using the coordinate system. It is also known as analytic geometry or Cartesian geometry.

To install an ironing board cabinet in a 60cm wide space, the minimum dimensions required for the depth and height of the cabinet would be:

Depth: The cabinet needs to be deep enough to accommodate the ironing board base, which is 38cm wide. Adding a few centimeters for clearance and ease of use, a depth of at least 50cm would be recommended.

Height: The cabinet needs to be tall enough to fit the entire height of the ironing board, which is 135cm. Adding a few centimeters for clearance and to ensure that the board fits comfortably inside the cabinet, a height of at least 140cm would be recommended.

Therefore, the minimum dimensions for the cabinet would be 60cm (width) x 50cm (depth) x 140cm (height).

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A metallic cube of length 15 cm is melted to form smaller cubes of 5 cm. How many smaller cubes will be there?

Answers

There will be 27 smaller cubes of length 5 cm each.

How to get the cubes

V = s^3, where s is the length of a side of the cube.

In this case, the length of the side of the original cube is 15 cm, so its volume is:

V = 15^3 = 3,375 cubic cm

When the cube is melted down and reformed into smaller cubes of 5 cm, the number of smaller cubes is equal to the total volume of the original cube divided by the volume of each smaller cube. The volume of each smaller cube is:

V = s^3 = 5^3 = 125 cubic cm

So, the number of smaller cubes is:

Number of smaller cubes = Total volume of original cube / Volume of each smaller cube

Number of smaller cubes = 3,375 / 125

Number of smaller cubes = 27

Therefore, there will be 27 smaller cubes of length 5 cm each.

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Given: LABC
Prove: The sum of the interior angle measures of AABC is 180°
E
O
3
N
Statement
1. Let points A, B, and C form a
triangle.
2. Let DE be a line passing
through B, parallel to AC
with angles as labeled.
4. m1m24, and
m23=m25
3
given
Reason
defining a parallel line and labeling angles
Congruent angles have equal measures.

Answers

The missing step is:

<1 ≅ <1 and <3 ≅ <5

Reason:

Alternate interior angles theorem

What is the alternate interior angles theorem?

The Alternate Interior Angles Theorem is a geometric proposition demonstrating the number of angles born when two parallel lines are intersected by an angled transversal.

Precisely expressed, it holds that whenever two lines of equivalence are cut by a straight line crossing them, the alternate interior angles (angles on both sides of the transversal, which lie inside the parallel lines) will be identical in measure.

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Please help me with the question

Answers

The answer is C

Explanation:

The formula for the volume of a cone is 1/3(pi)r^2*h

Since it’s is in pi units you can disregard the pi part and focus on 1/3r^2*h

And since the height is six and the volume is 36, you divide 36 by 6 to get 6.

Finally since the radius is squared in the formula and you need a value of six, answer c is the only option that works

Hope this helps!

When comparing three or more populations means within a set of quantitative data that is categorized according to one​ factor/treatment, a​ one-way ANOVA is appropriate.a. It is also appropriate in this​ situation, however, to compare two means at a time using multiple independent two sample​ t-tests. b. It is appropriate to compare two means at a time with independent two sample​ t-tests but it might be​ time-consuming.c. It is not appropriate to compare two means at a time in the way described. This would inflate the overall Type I Error and is a​ 'Multiple Testing' problem. The​ one-way ANOVA controls for the Type I Error and should be used instead.

Answers

According one-way ANOVA, the test is false.

We learn about one-way ANOVA

"One-Way ANOVA, also known as "analysis of variance," examines the refers to two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."

According to the given information, it is inappropriate to compare two means at a time using multiple independent two sample​ t-tests. It will create multiple testing problem and error.

So using one way ANOVA test when comparing three or more populations refers to within a set of quantitative data that is categorized according to one​ factor/treatment and compare two means at a time using multiple independent two sample​ t-tests is false.

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An airplane flies 1062 km with the wind. In the same amount of time it can fly 738 km against the wind. The speed of the plane in still air is 200km/h. Find The speed of the wind

Answers

The speed of the wind is approximately 18.8 km/h.

Now, let's use the information we have to set up some equations. We know that the distance the airplane can fly with the wind is 1062 km, and that it covers this distance in the same amount of time as it takes to fly 738 km against the wind. We can use the formula:

distance = speed x time

to write equations for these situations. For example, when flying with the wind:

1062 = (200 + w) x time

And when flying against the wind:

738 = (200 - w) x time

Now, we can solve for the unknown variable, which in this case is the speed of the wind. Let's rearrange the first equation to solve for time:

time = 1062 / (200 + w)

And the second equation:

time = 738 / (200 - w)

Since the time for each trip is the same, we can set these two expressions equal to each other and solve for w:

1062 / (200 + w) = 738 / (200 - w)

To solve for w, we can cross-multiply and simplify:

1062(200 - w) = 738(200 + w)

212400 - 1062w = 147600 + 738w

3442w = 64799

w = 18.8

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A bag contains 10 red pens, 15 blue pens, and 20 black pens. Joseph will pull a pen from the bag.
If Joseph pulls a red pen from the bag and he keeps the pen, is the probability of him selecting another red pen after a second pull an independent or dependent event? Explain.

Answers

Answer:

I can solve it, but you'll have to find out, because it's your homework, if it is an independent or dependent event:

9/(9 + 15 + 20)  -->  because we want to know chances of a red pen (qty 9)

9/(24 + 20)

9/44

0.2045454..., approx. 0.2045, or 20.45%

Answer: Hello!

Step-by-step explanation:

If no one can do it, I'll try.

This scenario is an example of dependent probabilities because the outcome of the second draw depends on what happened during the first draw. Specifically, if Joseph drew a red pen during the first draw, then there are fewer red pens remaining in the bag than before the first draw. As a result, the probability of drawing a red pen during the second draw decreases relative to the initial probability, assuming all pens were equally likely to be drawn initially. If the first pull didn't remove any pens from the bag, then the second pull is an independent event, and the probability remains unchanged.

In summary, whether the second event is independent or dependent depends on how many red pens remain in the bag after the first draw.

2. The table shows values that represent a function.

x
–2
–3
6
7
5

y
4
2
1
3
4
Part I: Write values that represent the inverse of the function represented in the table above. (3 points)
x

y

Part II: Is the inverse a function? Explain your answer. (2 points)
Remember that in a function, each input value can have only one output value.

Answers

To find the inverse of a function, we switch the x and y values. So the values representing the inverse of the function in the table above are: x: 4, 2, 1, 3, 4, and y: -2, -3, 6, 7, 5.

To determine if the inverse is a function, we need to check if each input value has only one output value.

Since the original function is a function, we know that each input value has only one output value.

When we switch the x and y values to find the inverse, we need to make sure that each y value only has one corresponding x value.

Looking at the values in the table, we can see that there are two different y values (4 and -2) that both have an x value of 5.

Therefore, the inverse is not a function.

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Solving a word pro
To rent a certain meeting room, a college charges a reservation fee of $19 and an additional fee of $4 per hour. The chemistry club wants to spend less than
$51 on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room?
User for the number of hours.
Write your answer as an inequality solved for t.

Answers

The possible numbers of hours the chemistry club could rent the meeting room is any value less than 8.

In inequality form:

t < 8

To solve this problem

Let's begin by referring to the number of hours the chemical club rents the meeting space as "t".

The reservation charge plus the additional fee for the specified number of hours will equal the total cost to rent the meeting space:

Cost in total = $19 + $4.

The chemical club has stated that they want to pay less than $51 to rent the space:

Total cost < $51

Substituting the expression for total cost:

$19 + $4t < $51

Simplifying:

$4t < $32

Dividing both sides by 4:

t < 8

Therefore, the possible numbers of hours the chemistry club could rent the meeting room is any value less than 8.

In inequality form:

t < 8

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