To make a profit of $281, the number of tickets that need to be sold is 150.
What is the minimum number of tickets that need to be sold in order to achieve a profit of $281?The profit from selling local ballet tickets can be determined by using the given function: [tex]p = -0.25x^2 + 0.30x + 6[/tex].
To find the number of tickets required to achieve a profit of $281, we can set p equal to 281 and solve for x. This results in a quadratic equation that can be solved using the quadratic formula.
Once we obtain the two possible values of x, we can select the positive value which represents the ticket price. Using this ticket price, we can then calculate the number of tickets required to achieve a profit of $281, which is 150.
In order to increase the profit, we can try adjusting the ticket price or increasing the number of tickets sold. However, it is important to keep in mind that there may be practical limits to both of these options.
For example, increasing the ticket price too much may deter customers from purchasing tickets, while increasing the number of tickets sold may require additional marketing efforts or larger venues.
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A group of 6 friends went to the movies. In addition to their tickets, they bought a large bag of popcorn to share for $9. 50. The total was $54. 50. Complete parts a and b
Answer:
Step-by-step explanation:
a) Let x be the cost of each ticket. Then the total cost of the tickets for the 6 friends is 6x. The total cost, including the popcorn, is $54.50. So we can set up an equation:
6x + $9.50 = $54.50
Solving for x, we get:
6x = $45.00
x = $7.50
So each ticket costs $7.50.
b) To find the cost per person, we need to add up the cost of each ticket and divide by the number of people. The cost of all 6 tickets is:
6 tickets × $7.50/ticket = $45.00
Adding the cost of the popcorn, we get:
$45.00 + $9.50 = $54.50
So the total cost for the 6 friends is $54.50, and the cost per person is:
$54.50 ÷ 6 people = $9.08 per person.
Therefore, each person contributed $9.08 towards the total cost of the tickets and popcorn.
Is these cosine or tangent or sine ? I need help with them can somebody tell me the answer to all three
Answer:
Step-by-step explanation:
I assume the question is what trig function do you use to find x? If that's correct then answers, from TOP to BOTTOM, are:
tan
cos
sin
Answer:
Triangle 1: tangent
Triangle 2: cosine
Triangle 3: sine
Step-by-step explanation:
First, some definitions before working the problem:
The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:
[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]
[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]
[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]
One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.
The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.
Triangle 1
For the first triangle, the known acute angle is in the bottom left. The two sides of the triangle that are known or are a "goal to find" are not the hypotenuse, so they are the "opposite" & "adjacent".
Specifically, the side of length "13" is touching the known acute angle AND the right angle, so it is the adjacent side. The unknown side of length "x" is is touching the right angle but is NOT touching the known acute angle, so it is the "opposite" (across from the angle).
Out of "Soh Cah Toa," the part that uses o & a is "Toa". The "T" in "Toa" stands for Tangent. So, the desired function to use for the first triangle is the Tangent function.
Triangle 2
For the second triangle, the known acute angle is in the top left. This time, the "adjacent" side is unknown, labeled as x, so it is the "goal to find" side. The "hypotenuse" is known.
Therefore, the two sides of the triangle that are known or are a "goal to find" are the "adjacent" & "hypotenuse".
Out of "Soh Cah Toa," the part that uses "a" & "h" is "Cah". So, the desired function to use for the first triangle is the Cosine function.
Triangle 3
For the third triangle, the known acute angle is in the top right.
This time, the side (at the bottom) across from the angle (at the top right) is known -- the "opposite" leg. Additionally, the "hypotenuse" is unknown and is our "goal to find" side.
Therefore, the two sides of the triangle that are known or are a "goal to find" are the "opposite" & "hypotenuse".
Out of "Soh Cah Toa," the part that uses "o" & "h" is "Soh". So, the desired function to use for the first triangle is the Sine function.
Lily's age is 2 years and 4 months.
Hugo's age is 1 year and 8 months.
Write Lily's age in months as a fraction of Hugo's age in months.
Give your answer in it's simplest form.
Answer:
7/5
Step-by-step explanation:
Lily's age in months: 2×12+4=28mo
Hugo's age in months=12+8=20
Lily's age over Hugo's age: 28/20
Simplify:
28/20=14/10=7/5
Victoria has $200 of her birthday gift money saved at home, and the amount is modeled by the function h(x) = 200. She reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1. 05)x−1. Explain how Victoria can combine the two functions to model the total amount of money she will have in her bank account as interest accrues after she deposits her $200. Justify your reasoning.
WILL GIVE BRANLIEST
The reasoning behind this is that the initial amount (h(x)) is multiplied by the interest growth factor (s(x)) to calculate the total amount with interest over time.
To model the total amount of money Victoria will have in her bank account as interest accrues after depositing her $200, you can combine the two functions h(x) and s(x). The given functions are h(x) = 200 and s(x) = (1.05)^x−1.
First, note that s(x) represents the growth factor of the interest, which is 5% (1.05) compounded annually. To find the total amount after x years, you need to multiply the initial amount by the growth factor raised to the power of x.
So, the combined function T(x) can be written as T(x) = h(x) * s(x).
Substitute the given functions into the combined function:
T(x) = (200) * ((1.05)^x−1)
This function, T(x), models the total amount of money Victoria will have in her bank account after x years with interest accrued on her $200 deposit. The reasoning behind this is that the initial amount (h(x)) is multiplied by the interest growth factor (s(x)) to calculate the total amount with interest over time.
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Write an exponential regression function to model the situation.
The exponential regression function to model the situation above is: y = 400,000(0.841)^x
What is the explanation for the above response?The exponential regression function to model the situation is:
y = ab^x
where,
y = flour in grams
x = number of weeks since the bakery opened
a = initial amount of flour (Y-intercept) = 400,000 grams
b = growth factor
To find the value of b, we can use any two points from the table. Let's use the first and second points.
When x = 0, y = 400,000
When x = 1, y = 336,400
Substituting these values in the equation, we get:
400,000 = ab^0
336,400 = ab^1
Simplifying these equations, we get:
a = 400,000
b = 0.841
Therefore, the exponential regression function is:
y = 400,000(0.841)^x
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You find an apartment which charges $925 a month rent. each year the rent increases by 6%.
The monthly rent for the apartment would be $1238.84 in the fifth year.
What is the monthly rent for an apartment that charges $925 initially and increases by 6% each year?The problem states that the monthly rent for an apartment is $925. To calculate the rent for the second year, we need to increase this amount by 6%.
To do this, we first need to calculate 6% of $925. We can do this by multiplying 0.06 (which is equivalent to 6%) by $925:
6% of $925 = 0.06 × $925 = $55.50
So, the rent for the second year would be:
$925 + $55.50 = $980.50
To find the rent for the third year, we need to increase the rent for the second year by 6%. We can follow the same process:
6% of $980.50 = 0.06 × $980.50 = $58.83
So, the rent for the third year would be:
$980.50 + $58.83 = $1039.33
To find the rent for any year n, we use the formula:
Rent for year n = $925 × (1 + 0.06)^n
In this formula, (1 + 0.06) represents the multiplier used to calculate the new rent each year.
For example, the multiplier for the second year is 1 + 0.06 = 1.06, and the multiplier for the third year is 1.06 × 1.06 = 1.1236 (rounded to four decimal places).
To find the rent for the fifth year, we plug in n = 5:
Rent for year 5 = $925 × (1 + 0.06)^5 = $925 × 1.3382 = $1238.84 (rounded to the nearest cent)
So, the monthly rent for the apartment would be $1238.84 in the fifth year.
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Select the correct answer. team goal scored in first five minutes p 2.34% q 3.56% r 1.24% s 4.01% t 3.88% total 2.86% the probabilities of a particular soccer team scoring a goal within the first five minutes of the game are given in the table. what is the probability of a goal being scored in the first five minutes of the game, given that the team is team q? a. 1.24% b. 2.86% c. 3.56% d. insufficient data
The probability of a goal being scored in the first five minutes of the game, given that the team is team q is 1.24%. The correct option is a.
The probability of a goal being scored in the first five minutes of the game, given that the team is team q, is given by the conditional probability:
P(goal scored in first 5 min | team is q) = P(goal scored in first 5 min and team is q) / P(team is q)
From the table, we have:
P(goal scored in first 5 min and team is q) = 3.56%
P(team is q) = 3.56%
Therefore:
P(goal scored in first 5 min | team is q) = 3.56% / 3.56% = 1
This means that if we know the team is team q, the probability of a goal being scored in the first five minutes of the game is 100% (or certain). So the correct answer is (a) 1.24%.
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The lengths of the sides of triangle XYZ are written in terms of the variable m, where m ≥ 6.
Triangle X Y Z is shown. The length of side X Y is m + 8, the length of side Y Z is 2 m + 3, the length of side Z X is m minus 3.
Which is correct regarding the angles of the triangle?
mAngleX < mAngleZ < mAngleY
mAngleY < mAngleZ < mAngleX
mAngleY < mAngleX < mAngleZ
mAngleZ < mAngleY < mAngleX
Answer:
In a triangle, the side opposite to the largest angle is the longest side, and the side opposite to the smallest angle is the shortest side. In triangle XYZ, the length of side XY is m + 8, the length of side YZ is 2m + 3, and the length of side ZX is m - 3. Since m ≥ 6, we can determine that 2m + 3 is the largest value, m + 8 is the next largest value, and m - 3 is the smallest value. Therefore, side YZ is the longest side and side ZX is the shortest side.
Since side YZ is the longest side, angle X must be the largest angle. Since side ZX is the shortest side, angle Y must be the smallest angle. Therefore, the correct ordering of the angles from smallest to largest is ∠Y < ∠Z < ∠X.
Step-by-step explanation:
if an airplane travels around the world, flying just above the equator it would travel 1.25 x 10^4 miles. How many miles would a plane travel if it flew around the world just above the equator 3 1/2 times?
(in standard form)
A plane flying just above the equator around the world 3 1/2 times would cover a distance of 4.375 x 10⁴ miles.
If an airplane travels around the world just above the equator once, it covers a distance of 1.25 x 10⁴ miles. To find how many miles it would cover if it flew around the world 3 1/2 times, we need to multiply this distance by 3.5:
1.25 x 10⁴ miles x 3.5 = 4.375 x 10⁴ miles
To understand this calculation, we need to know that 3 1/2 times means 3.5 times. So, we multiply the distance covered in one round of the world by 3.5 to find the total distance covered in 3 1/2 times around the world.
We use standard form to express the answer in a more compact and convenient way, where 4.375 x 10⁴ represents the number 43,750 in scientific notation.
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A 2-quart carton of pineapple juice costs $8.08. What is the price per cup?
$
Answer:
$1.01
Step-by-step explanation:
We Know
A 2-quart carton of pineapple juice costs $8.08
1 quart = 4 cups
2 quarts = 8 cups
So, 8 cups of pineapple juice cost $8.08.
What is the price per cup?
We Take
8.08 / 8 = $1.01
So, the price per cup is $1.01
Samantha is told that sin (O) = and tan (0)<0, and was asked to determine the value of cos (©).
• She uses the Pythagorean identity and defines it to be sin() + cos2 ( 0 )= 1.
• She substitutes į into the equation for sin (0)
• She then looks at values of sin ( ) and tan () and says that the only quadrant in which sin() is positive and
tan() is negative is the first quadrant.
Samantha determines that the answer is
cos () =
(21)
Samantha determines the answer as cos(θ) = -√(3/4).
Based on the information given, I can help you with this problem. Samantha is correct in using the Pythagorean identity and substitution, but she made an error in identifying the quadrant. Here's the correct process:
1. Given sin(θ) = 1/2 and tan(θ) < 0.
2. The correct quadrant where sin(θ) is positive and tan(θ) is negative is the second quadrant, not the first.
3. Using the Pythagorean identity: sin^2(θ) + cos^2(θ) = 1.
4. Substitute sin(θ) = 1/2 into the equation: (1/2)^2 + cos^2(θ) = 1.
5. Simplify: 1/4 + cos^2(θ) = 1.
6. Solve for cos^2(θ): cos^2(θ) = 3/4.
7. Since we are in the second quadrant, cos(θ) is negative: cos(θ) = -√(3/4).
Your answer: cos(θ) = -√(3/4).
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Susan got a prepaid debit card with 20 on it.For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 16 cents per yard. If after that purchase there was 14.88 left on the card, how many yards of ribbon did Susan buy?
Answer:
32 yards
Step-by-step explanation:
Let's see, the card started out with $20 on it, and ended up with $14.88.
To find how much she spent on ribbon, we can first subtract the 2 amounts:
20-14.88
=5.12
So, Susan spent $5.12 on ribbon. We also know that each yard of ribbon was $0.16, so we can divide the spent amount ($5.12) by $0.16 to find out how many yards she bought:
5.12/0.16
=32
So, Susan bought 32 yards of ribbon.
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Assume that a cell is a sphere with radius 10-3 or 0.001 centimeter, and that a cell’s density is 1.1 grams per cubic centimeter. koalas weigh 6 kilograms on average. how many cells are in the average koala? hippos weigh 1,400 kilograms on average. how many cells are in the average hippo? solution
There would be 1.302 x 10¹² cells in koala, and there are 3.04 x 10^17 cells in the average hippo.
To find the number of cells in the average koala, we first need to find the volume of the koala in cubic centimeters, since we know the density of the cell and can use that to find the mass of the koala in grams.
The average weight of a koala is 6 kilograms, which is equivalent to 6,000 grams. We can use the density of the cell to find the volume of the koala:
Density = Mass / Volume
1.1 g/cm³ = 6,000 g / Volume
Volume = 6,000 g / 1.1 g/cm³
Volume = 5,454.54 cm³
Next, we need to find the volume of one cell:
Volume of cell = 4/3 * π * (0.001 cm)³
Volume of cell = 4.188 x 10⁻⁹ cm³
Finally, we can divide the volume of the koala by the volume of one cell to find the number of cells in the average koala:
Number of cells = 5,454.54 cm³ / (4.188 x 10⁻⁹ cm³)
Number of cells = 1.302 x 10¹²
Therefore, there are approximately 1.302 x 10¹² cells in the average koala.
To find the number of cells in the average hippo, we can follow the same process. The average weight of a hippo is 1,400 kilograms, which is equivalent to 1,400,000 grams. Using the density of the cell, we can find the volume of the hippo:
Density = Mass / Volume
1.1 g/cm^3 = 1,400,000 g / Volume
Volume = 1,400,000 g / 1.1 g/cm³
Volume = 1,272,727.27 cm³
Dividing the volume of the hippo by the volume of one cell, we get:
Number of cells = 1,272,727.27 cm³ / (4.188 x 10⁻⁹ cm³)
Number of cells = 3.04 x 10¹⁷
Therefore, there are approximately 3.04 x 10¹⁷ cells in the average hippo.
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This equation shows how the cost of a plumber's visit is related to its duration in hours. C = 51d
The variable d represents the duration of the visit in hours, and the variable c represents the cost. If a plumber's visit lasted 1 hour, how much would it cost?
The cost of a plumber's one-hour visit is $51, determined by the linear equation C = 51d, where C is the cost and d is the duration of the visit in hours.
How is the cost of a plumber's visit determined by duration?If a plumber's visit lasts for a certain duration, the cost can be determined using the equation
C = 51d
where C is the cost and d is the duration of the visit in hours.
In this case, the duration of the plumber's visit is given as 1 hour. Substituting d = 1 in the equation, we get
C = 51(1) = $51
as the cost of the plumber's visit.
Therefore, if the plumber's visit lasts for one hour, it would cost $51 according to the given equation.
This cost may vary if the duration of the visit changes, as it is directly proportional to the duration of the visit.
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During the basketball game, you record the number of rebounds from missed shots for each team. (a) describe the likelihood that your team rebounds the next missed shot. (B) how many rebounds should ur team expect to have in 15 missed shots
In the event of describing the likelihood that the team rebounds the next missed shot is likely, and the number of rebounds that the team should expect to have missed in 15 shots is 10.5 rebounds.
Given
Number of shots missed by the given team is 7
Total number of shots fired is 10
a) Then, moving on to the first part of the question
Here we have to apply probability to evaluate the likelihood of the given team rebounds the next missed shot.
Then,
Probability = no of shots attended / total number of shots fired
Probability = 7 /10
Then the event is likely
b) Now the second part
Then the number of rebounds the given team expect to have in the next 15 missed shots
= 7/10 ×15
= 105/10
= 10.5 rebounds
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If 2/3 of a mini pizza cost $2. 40, what would 1/2 of a mini pizza cost?
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
1/2 of a mini pizza would cost $0.60.
If 2/3 of a mini pizza cost $2.40, then 1/3 of a mini pizza would cost half of that:
1/3 of a mini pizza = 1/2 * $2.40 = $1.20
To find the cost of 1/2 of a mini pizza, we can divide the cost of 1/3 of a mini pizza by 2:
1/2 of a mini pizza = 1/2 * $1.20 = $0.60
Therefore, 1/2 of a mini pizza would cost $0.60.
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Which of the equations shown have infinitely many solutions? Select all that apply. A. 3x – 1 = 3x + 1 B. 2x – 1 = 1 – 2x C. 3x – 2 = 2x – 3 D. 3(x – 1) = 3x – 3 E. 2x + 2 = 2(x + 1) F. 3(x – 2) = 2(x – 3)
The two equations with infinite solutions are D 3(x – 1) = 3x – 3 and E2x + 2 = 2(x + 1)
Which equations have infinite solutions?An equation has infinite solutions if we can remove the dependence of the variable, and we end with a true equation.
For example, option D is:
3(x - 1) =3x - 3
Expanding the left side:
3x - 3 = 3x - 3
Subtract 3x in both sides:
-3 = -3
That is true for any value of x.
The other correct option is E:
2x + 2 = 2(x + 1)
2x + 2 = 2x + 2
2 = 2
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h=-16t^2+27t+3 what is the max height of the soccer ball
To find the maximum height of the soccer ball, we need to determine the vertex of the quadratic function. The vertex is given by the formula:
t = -b/2a
where a = -16 and b = 27 from the given equation:
H = -16t^2 + 27t + 3
Substituting these values into the formula, we get:
t = -27/(2(-16)) = 0.84375
Now that we have the value of t at the vertex, we can find the maximum height by substituting it back into the original equation:
H = -16(0.84375)^2 + 27(0.84375) + 3 = 12.65625
Therefore, the maximum height of the soccer ball is approximately 12.65625 units.
h = -16t^2 + 27t + 3 = -(4t - 27/8)^2 + 921/64
With every number t, h [tex]\leq[/tex] 921/64.
Therefore, the maximum height of the soccer ball is 921/64, or aprroximately 14.4(units)
"=" when 4t = 27/8, or t = 27/32.
Josh and Draven can clean the JHS cafeteria in 25 minutes. Draven can clean the JHS cafeteria in 40 minutes. How long will it take Josh to do the job if he works alone?
It will take Josh about 66.67 minutes to easy the cafeteria alone.
Let's anticipate that the amount of work required to easy the cafeteria is 1 unit.
In a single minute, Josh can easy 1/x of the cafeteria (in which x is the number of mins it takes Josh to do the task alone), and Draven can clean 1/40 of the cafeteria in one minute.
When they work together, they could easy the cafeteria in 25 minutes, so in one minute they are able to easy 1/25 of the cafeteria.
The use of the fact that their combined rate is the sum in their individual rates, we are able to installation an equation:
1/x + 1/40 = 1/25
Multiplying each facets through the least common more than one of the denominators (40 * 25 * x), we get:
25 * 40 + x * 40 = x * 25
1000 + 40x = 25x
15x = 1000
x = 66.67
Therefore, it'd take Josh about 66.67 minutes to easy the cafeteria alone.
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What is the value of B? Bº 58° 61°
Answer:
61 degrees
Step-by-step explanation:
Triangle interior measures add up to 180 degrees.
61 + 58 + x = 180
119 + x = 180
x = 61
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The bulldogs, a baseball team, has nine starting players the height of the starting players are 72in 71in 78in 70in 72in 72in 73in 70in and 72 in which team best describes the data value 78 in
The value 78 inches best describes the tallest player on the Bulldogs baseball team. This height is an outlier within the data set and may affect statistical analyses.
The Bulldogs, a baseball team, consists of nine starting players with varying heights. Their heights are as follows: 72 in, 71 in, 78 in, 70 in, 72 in, 72 in, 73 in, 70 in, and 72 in. To describe the data, we can analyze the presence of the 78 in height value.
In this case, the value 78 in represents the tallest player on the team. When examining this data set, it is important to understand how this value affects the overall distribution of heights among the players. One way to determine this is by calculating the mean, median, and mode of the height data.
The mean (average) height for the team is 71.22 inches, and the median (middle) value is 72 inches. The mode (most frequent) height is also 72 inches. The value 78 inches is above the mean and median values, indicating that it is an outlier, or a value that is significantly different from the majority of the other data points.
In conclusion, the value 78 inches best describes the tallest player on the Bulldogs baseball team. This height is an outlier within the data set and may affect statistical analyses. However, it provides valuable information about the diversity of heights among the starting players on the team.
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On Thursday,30 scholars went to morning homework help. On Friday, 24 scholars went. What is the percent decrease in the number of scholars who went to morning homework help from Thursday to Friday?
PLEASE HELP 20 POINTS
There is 20% decrease in scholars number who went to the morning homework help.
What is the percent decrease?To get the scholar's percent decrease, we need to calculate the difference between them on Thursday and Friday and theb divide that by the number of scholars on Thursday.
Data:
Number of scholars on Thursday = 30
Number of scholars on Friday = 24
Difference = 30 - 24 = 6
The percent decrease = (6/30) x 100%
The percent decrease = 0.2 * 100%
The percent decrease = 20%
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Ying Yu bought a rectangular box to display her doll collection. She decided
to exchange the box for a similar one that had five times its dimensions.
How does the volume of the larger rectangular box compare to the volume
of the smaller box?
The volume of the larger rectangular box is 125 times the volume of the smaller box.
To compare the volume of the larger rectangular box to the smaller box, we need to consider how the dimensions have changed.
Since the larger box has dimensions 5 times those of the smaller box, let's represent the dimensions of the smaller box as length (L), width (W), and height (H). Therefore, the dimensions of the larger box would be 5L, 5W, and 5H.
Now, let's calculate the volume of both boxes:
1. Volume of the smaller box: V_small = L * W * H
2. Volume of the larger box: V_large = (5L) * (5W) * (5H)
To find the ratio of the larger box's volume to the smaller box's volume, we can divide the volumes:
V_large / V_small = ((5L)*(5W)*(5H)) / (L * W * H)
Notice that L, W, and H can be canceled out:
(5 * 5 * 5) = 125
So, the volume of the larger rectangular box is 125 times the volume of the smaller box.
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One medical procedure used today allows parents to select the gender of their future baby. The procedure has been found to be effective 75% of the time, meaning that 75% of the time parents get a baby of the preferred gender. Suppose this method is used by 5 couples at one particular clinic. For #6 and 7, write the numeric value and write in words what it represents
6. The probability that all 5 couples will have a baby of the preferred gender is 0.2373.
7. The probability that at least 4 of the 5 couples will have a baby of the preferred gender is 1 - 0.3672 = 0.6328.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to predict with absolute certainty.
6. What is the probability that all 5 couples will have a baby of the preferred gender?Answer: The probability that one couple will have a baby of the preferred gender is 0.75. Assuming the gender of each baby is independent of the others, the probability that all 5 couples will have a baby of the preferred gender is 0.75⁵ = 0.2373.
Numeric value: 0.2373
In words: The probability that all 5 couples will have a baby of the preferred gender is 0.2373.
7. What is the probability that at least 4 of the 5 couples will have a baby of the preferred gender?Answer: There are two ways to approach this problem. One way is to calculate the probability of each possible outcome (0 to 5 couples having a baby of the preferred gender) and then add up the probabilities for the outcomes where at least 4 couples have a baby of the preferred gender. Another way is to use the complement rule and subtract the probability that fewer than 4 couples have a baby of the preferred gender from 1.
Using the first method, we can calculate the probabilities as follows:
- 0 couples: 0.25⁵ = 0.0009766
- 1 couple: 5 x 0.75 x 0.25⁴ = 0.01465
- 2 couples: 10 x 0.75² x 0.25³ = 0.08789
- 3 couples: 10 x 0.75³ x 0.25² = 0.2637
- 4 couples: 5 x 0.75⁴ x 0.25 = 0.3955
- 5 couples: 0.75⁵ = 0.2373
The probabilities for the outcomes where at least 4 couples have a baby of the preferred gender are 0.3955 and 0.2373, so the total probability is 0.3955 + 0.2373 = 0.6328.
Using the second method, we can calculate the probability that fewer than 4 couples have a baby of the preferred gender as follows:
- 0 couples: 0.25⁵ = 0.0009766
- 1 couple: 5 x 0.75 x 0.25⁴ = 0.01465
- 2 couples: 10 x 0.75² x 0.25³ = 0.08789
- 3 couples: 10 x 0.75³ x 0.25² = 0.2637
The probability that fewer than 4 couples have a baby of the preferred gender is the sum of these probabilities: 0.0009766 + 0.01465 + 0.08789 + 0.2637 = 0.3672.
Therefore, the probability that at least 4 of the 5 couples will have a baby of the preferred gender is 1 - 0.3672 = 0.6328.
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A spinner with 6 equally sized slices has 6 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellow slice?
Answer:
1
Step-by-step explanation:
Which expression is equivalent to 6\cdot 6^{-2}\normalsize?6⋅6
−2
?
The expression 6 * 6^(-2) is equivalent to 1/6.
Simplify this expression using the rule of exponents?We can simplify this expression using the rule of exponents that states a^m / a^n = a^(m-n), which gives:
6 * 6^(-2) = 6 / 6^2 = 6 / 36 = 1/6
Let's break down the expression and simplify it step by step:
6 * 6^(-2)
We start by evaluating the exponent, which means we take the reciprocal of 6^2:
6 * (1/6^2)
Now we simplify the denominator of the fraction:
6 * (1/36)
Finally, we can simplify the expression by dividing 6 by 36:
1/6
So, the expression 6 * 6^(-2) is equivalent to 1/6. This means that if we multiply 6 by 6 raised to the power of -2 (or 1/6^2), we get the same result as dividing 6 by 6^2 (or 36), which is 1/6.
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on yellow, P(not yellow).
The theoretical probability of the spinner not landing on yellow, would be 75 %.
How to find the probability ?In order to calculate the likelihood of the spinner not landing on yellow, it is necessary to initially identify the quantity of non-yellow partitions and subsequently divide this by the full tally of sections. The spinner comprises a total of 8 individual segments.
Of these, two (i.e., sections 2 and 3) are colored in shades of yellow, hence totaling two yellow sectors. This leaves a further six compartments - numbered 1, 4, 5, 6, 7 and 8, that do not fall into the category of "yellow."
The probability is therefore :
= ( Number of not yellow sections ) / ( Total number of sections )
= 6 / 8
= 3 / 4
= 75 %
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In 2000, 1500 rabbits live in a warren in a certain area. the number of rabbits increases exponentially at a discrete rate of 7% per year. predict population in 2008&2022
The predicted populations of rabbits in the warren in 2008 and 2022 are 2909 and 9933, respectively.
To predict the population of rabbits in the warren in 2008 and 2022, we can use the formula for exponential growth:
P(t) = P₀ (1 + r)ᵗ
Where P(t) is the population at time t, P₀ is the initial population, r is the growth rate, and t is the time elapsed.
For this problem, we know that P₀ = 1500, r = 0.07 (since the growth rate is 7%), and we want to find P(8) and P(22) (since we're predicting the population in 2008 and 2022, respectively).
Using the formula, we get:
[tex]P(8) = 1500( 1 + 0.07)^{8} = 2909[/tex]
So we can predict that there will be about 2909 rabbits in the warren in 2008.
To find P(22), we simply plug in t = 22:
[tex]P(22) = 1500 (1 + 0.07)^{22} = 9933[/tex]
So we can predict that there will be about 9933 rabbits in the warren in 2022.
Therefore, the predicted populations of rabbits in the warren in 2008 and 2022 are 2909 and 9933, respectively.
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11. The spread of a drop of food dye throughout a glass of milk is called__________
Answer: Diffusion
Step-by-step explanation:
Analyze the diagram below and answer the questions that follow.
F
G
t
How many different ways can the line above be named? What are those names?
A. 2 ways; FG, GF
B. 3 ways; t, FG, GF
C. 4 ways; t, FG, FG, GF
D. 5 ways; t, FG, GF, FG GF
Answer: A. 2 ways; FG, GF
Step-by-step explanation: There are only two ways to name a line, and they are interchangeable: starting from one endpoint and naming the other endpoint second, or starting from the second endpoint and naming the first endpoint second.
