The volume of prism P is calculated as: 16.55 cm³.
What is the volume of the prism?Similar figures are defined as those figures that the same shape, but the sizes are different.
The parameters given are:
- Prism P and prism Q are similar.
- Ratio of the surface area of the prism P to Q = 1 : 3
We also have:
Volume of prism Q = 86 cm³
Scale factor of height of the prism would be square root of surface area of the prism.
Scale factor of volume of the prism would be the cube of the height of the prism.
Let volume of prism P be V(P)
Let the volume of the prism Q be V(Q).
Thus:
V(P) / V(Q) = 1 / (√3)³
V(P) = V(Q) / (√3)³
= 86 / (√3)³
= 16.55 cm³
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The maximum capacity for sedating in a theater is 500 people. The theater sells two types of tickets, adult tickets for 7.25 each and child tickets for 4 each. If they sold out on a certain showtime and made a total of 3157 in ticket sales, how many of each type was sold for that showtime
he theater sold 356 adult tickets and 144 child tickets for a certain showtime to make a total of $3157 in ticket sales.
We have,
Let's assume that the number of adult tickets sold is x, and the number of child tickets sold is y.
We know that the total number of tickets sold cannot exceed the maximum capacity of the theater, so we have the inequality:
x + y ≤ 500
We also know that the total revenue from ticket sales is $3157, so we can write another equation based on the ticket prices:
7.25x + 4y = 3157
We have two equations with two variables, so we can solve for x and y using any method of our choice.
Here, we will use substitution.
We can write,
y ≤ 500 - x.
We can substitute this into the second equation.
7.25x + 4(500 - x) = 3157
Simplifying and solving for x.
7.25x + 2000 - 4x = 3157
3.25x = 1157
x = 355.69
We can't sell a fractional number of tickets, so we must round x to the nearest whole number.
Let's assume that x = 356.
Then, from the first inequality.
356 + y ≤ 500
y ≤ 144
Therefore, we can sell at most 144 child tickets.
To check if this solution satisfies the equation 7.25x + 4y = 3157, we substitute x = 356 and y = 144 into the equation:
7.25(356) + 4(144) = 3157
This is true, so our solution is valid.
Therefore,
The theater sold 356 adult tickets and 144 child tickets for a certain showtime to make a total of $3157 in ticket sales.
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suppose i have an organization that has 60 members, i'm going to pick one person at random to be the president, another person to be the vice president, and a third person to be the treasurer. how many ways can this be done?
There are 205,320 ways to select one person to be the president, one person to be the vice president, and a third person to be the treasurer from a group of 60 members.
The number of ways to select the president from the 60 members is 60, since any one of the 60 members can be chosen.
Once the president has been chosen, there are only 59 members left to choose from for the vice president. Therefore, there are 59 ways to select the vice president.
Similarly, after the president and vice president have been chosen, there are only 58 members left to choose from for the treasurer. Therefore, there are 58 ways to select the treasurer.
Using the multiplication principle of counting, the total number of ways to select one person to be the president, one person to be the vice president, and a third person to be the treasurer is
60 x 59 x 58 = 205,320
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Calcula cuál es el precio de un mantel cuadrado de 3,5 m² de lados y el metro cuadrado de la Cuesta 7,25 €
Based on the mentioned informations and provided values, the price of a square tablecloth with 3.5 m² sides and a cost of €7.25 per square meter is €88.81.
Calculate the price of a square tablecloth with 3.5 m² sides and the square meter of the cost €7.25
The area of the square tablecloth is:
Area = side x side = 3.5 m x 3.5 m = 12.25 m²
To calculate the price of the tablecloth, we need to multiply the area by the cost per square meter:
Price = Area x Cost per square meter
= 12.25 m² x €7.25/m²
= €88.81
Therefore, the price of a square tablecloth with 3.5 m² sides and a cost of €7.25 per square meter is €88.81.
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The complete question is :
Calculate the price of a square tablecloth with 3.5 m² sides if the per square meter cost of the cloth is €7.25.
If you arranged the cubes on the floor to make a square would the square fit in your classroom? What would it’s dimensions be? Explain your reasoning
The squares may or may not fit in the classroom, depending on the dimensions
Would the square fit in the classroom?The number of cubes is given as
Cubes = 1000000
The area of a square is
Area = Length^2
In this case, the number of cubes is the area
So, we have
Length^2 = 1000000
Take the square root of both sides
Length = 1000
This means that the dimensions would be 1000 by 1000
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Find the equation of a circle. Radius 5, Center (0,-5)
Answer:
(x−h)2+(y−k)2=r2
(x−0)^2+(y+5)^2=25
Step-by-step explanation:
the qualified applicant pool for two management trainee positions consists of four men and six women. if the applicants are equally qualified and the trainee positions are selected by drawing the names at random so that all groups of two are equally likely, what is the probability that the trainee class will consist entirely of men? round your answer to the nearest thousandth. group of answer choices 0.044 0.178 0.133 0.022 none of these choices
The probability that the trainee class will consist entirely of men is option (c) 0.133
To calculate the probability that the trainee class will consist entirely of men, we need to determine the total number of ways to select two people from the pool of ten applicants, as well as the number of ways to select two men from the pool of four men
The total number of ways to select two people from the pool of ten applicants is given by the combination formula
C(10, 2) = 10! / (2! × (10 - 2)!) = 45
This means that there are 45 different ways to select two people from the pool of ten applicants.
The number of ways to select two men from the pool of four men is given by the combination formula
C(4, 2) = 4! / (2! × (4 - 2)!) = 6
This means that there are 6 different ways to select two men from the pool of four men.
Therefore, the probability that the trainee class will consist entirely of men is given by the ratio of the number of ways to select two men from the pool of four men to the total number of ways to select two people from the pool of ten applicants
P(2 men) = C(4, 2) / C(10, 2) = 6/45 = 2/15
=0.133
Therefore, the correct option is (c) 0.133
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p is inversely proportional to t complete the table of values
The requried table of values for P inversely proportional to t has been shown below.
To complete the table of values for P inversely proportional to t, we need to use the formula for inverse proportion:
P = k/t
where k is the constant of proportionality. To find k, we can use any one of the given values of P and t. Let's use the first row of the table where P = 8 and t = 2:
8 = k/2
k = 16
Now we can use this value of k to find the corresponding values of P for the other values of t in the table:
t P
2 8
4 4
6 2.67
8 2
10 1.6
We can see that as t increases, P decreases, which is consistent with the behavior of inverse proportion.
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Question 3(Multiple Choice Worth 2 points)
(Scale Factor LC)
Figure 1 and figure 2 are right triangles.
two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 7 units long
What scale factor was used to produce Figure 2 from Figure 1?
7 over 3
3 over 7
7
3
The scale factor used to produce Figure 2 from Figure 1 is: 7/3. The correct option is 1.
A scale factor is a number in mathematics that scales or multiplies some quantity.
The scale factor in geometry refers to the ratio of the lengths of two corresponding sides of two similar geometric figures.
The scale factor is the ratio of two similar figures' corresponding sides. The two triangles in this case are similar because they have the same shape but different sizes.
Figure 2's legs are 7 units long, which is 7/3 the length of Figure 1's legs, which are 3 units long.
Thus, the scale factor used to generate Figure 2 from Figure 1 is 7/3.
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What is the measure of angle abc
Measure of angle ABC would be equal half measure arc of AB
angle ABC = 1/2 × 246
= 123
In art class students are mixing blue and red paint to make purple paint. Madelyn mixes 3 cups of blue paint and 10 cups of red paint. Arturo mixes 1 cup of blue paint and 4 cups of red paint. Whose purple paint will be redder?
Answer:
To compare the purple paints that Madelyn and Arturo made, you need to find the ratio of red to blue in each mixture. You can do this by dividing the amount of red paint by the amount of blue paint.
For Madelyn, the ratio of red to blue is:
10 / 3 = 3.33
For Arturo, the ratio of red to blue is:
4 / 1 = 4
Since Arturo has a higher ratio of red to blue, his purple paint will be redder than Madelyn’s.
Create two different algebraic expressions involving c and d that are worth 24.
c = 4.25
d = 3.75
Answer:
c and d are worth 24 if c4.285 and d 3.75 multiply c and d and divide 24
suppose that 60% of people receive their flu shot. if 7 people are selected at random. what is the probability that exactly 3 of them have obtained their flu shot?
The probability that exactly 3 of the 7 people selected at random have obtained their flu shot is approximately 0.315 or 31.5%.
How to calculate the probability?This problem can be solved using the binomial distribution, which models the probability of getting a certain number of successes (in this case, people who received their flu shot) in a fixed number of trials (in this case, selecting 7 people at random) when each trial has the same probability of success (in this case, 60%).
The probability of getting exactly 3 people who received their flu shot is given by the formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the total number of trials (7), k is the number of successes (3), p is the probability of success (0.6), and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.
Plugging in the values, we get:
P(X = 3) = (7 choose 3) * (0.6)^3 * (1-0.6)^(7-3)
= 35 * 0.216 * 0.4096
= 0.315
Therefore, the probability that exactly 3 of the 7 people selected at random have obtained their flu shot is approximately 0.315 or 31.5%.
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an object is dropped straight down from a helicopter. the object falls faster and faster but its acceleration is measured in ft/sec^2 and recorded every second after the drop for 5 seconds, as shown. Find the following estimates
Upper estimate for the speed when t=5
Lower estimate for the speed when t=5
Upper estimate for the distance fallen when t=3
After considering all the given data we conclude that the upper estimate regarding t= 5 is 74.65 ft/sec, the lower estimate regarding t = 5 is 45.28 ft/sec, the upper estimate regarding t = 3 is 63.18 ft.
It is known that acceleration of the object is measured in ft/sec² and measured every second after the drop for 5 seconds. The acceleration decreases over time because of air resistance.
The upper estimate for the speed when t=5 is 32+19.41+11.77+7.14+4.33= 74.65 ft/sec.
The lower estimate for the speed when t=5 is 19.41+11.77+7.14+4.33+2.63=45.28 ft/sec.
The upper estimate for the distance fallen when t=3 is 32+19.41+11.77=63.18 ft.
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Find the value of x. Assume that segments that appear to be tangent are tangent. * Round to the nearest tenth (one decimal place)* 9 13 X=00.0 X
Answer:
[tex] {x}^{2} = {9}^{2} + {26}^{2} [/tex]
[tex] {x}^{2} = 81 + 676 = 757[/tex]
[tex]x = \sqrt{757} = 27.5[/tex]
So x = about 27.5
The total population of the world has recently estimated to be 7300000 total land surface is approximately 1.5 x 10 ^ 8 km squared kilometers.Calculate the average number of people per km2
The average number of people per km2 is 0.0487
Calculating the average number of people per km2From the question, we have the following parameters that can be used in our computation:
Population = 7300000
Total land surface = 1.5 x 10 ^ 8 km squared kilometers
So, we have
Average number of people = Population/Total land surface
Substitute the known values in the above equation, so, we have the following representation
Average number of people = 7300000/(1.5 x 10 ^ 8)
Evaluate
Average number of people = 0.0487
Hence, the average number of people = 0.0487
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Label the angle that is 90º in this 2-dimensional figure.
answers:
A. acute
B. right
C. obtuse
Answer:
B. right-----------------
The 90° angle is:
∠G or ∠FGH, as it is marked by a small squareIt is also called a right angle.
Therefore the matching choice is B.
The table lists data on the hair length and the age of nine girls. Select the points that represent this data.
The points that represent this data are shown in the scatter plot attached below.
How to construct and plot the data in a scatter plot?In this scenario, the age (in years) would be plotted on the x-axis (x-coordinate) of the scatter plot while the hair length (in inches) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the age (in years) and the hair length (in inches), a linear equation for the line of best fit is given by:
y = 0.0502x + 7.73
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Chiang's soccer practice started at 2:25 p. M. And ended at 4:30 p. M. How long did the practice last?
Please help me with this question.
The radius and the circumeference of the first semicircle is 6 inches and 18.85 inches².
Given that the diameter of the semi-circle is 12 inches.
The radius is always half the diameter. Therefore, the radius of the given semi-circle is:
Radius of the semicircle = Diameter / 2
= 12 inches / 2
= 6 inches
The circumference of the semicircle is:
Circumference = π × r
= π × 6 in.
= 18.85 in
The area of the purple semicircle:
Area = (π/8) × d²
= (π/8) × 5²
= 9.817 inches²
The area of the blue semicircle:
Area = (π/8) × d²
= (π/8) × 5²
= 16.085 inches²
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4. A scale model of a building is 1 inch to 10 feet. If the building is 50 feet tall, how tall is the model?
The height of the model is 5 inches
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
The ratio of the model to the original building is
1in : 10 feet.
converting 10feet to inches
10feet = 120inches since 1 feet is 12 inches.
Therefore the ratio will be;
1: 120
therefore if the building is 50 feet tall
50 feet = 50×12 = 600inches
the model height = 600/120 = 5 inches
therefore the height of the model is 5 inches
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4 teacher surveys a random group of students about their preference for doing classwork online or on paper. The results are shown in the table below. STUDENT CLASSWORK PREFERENCE Preference Online Paper Number of Students 17 8 Based on the results, how many students out of 350 will most likely have a preference to do their classwork online? Show your work and 3 reads
1r: what is the problem about
2r: what is the question asking you
3r: connection with number
Answer:
3
Step-by-step explana
sorry if its wrong
The cost to buy lunch at school was $4 and is now $7. What is the percent of change?
Answer:
percentage of change=75%
Step-by-step explanation:
percent of change =(final-initial)/initial×100
now
percent of change=(7-4)/4×100
=3/4×100
=75%
someone pls help mee. theres 2 questions im just really stuck on
a) If the nth term of sequence 32,-8,2, aₙ = 3aₙ₋₂ - 2aₙ₋₃ and a₁ = 32.
b) If explicit formula is aₙ = -7+10(n-1), a₁ = -7 and aₙ = aₙ₋₁ + 10.
a) a₁ = 32 (the first term of the sequence is given)
aₙ = 3aₙ₋₂ - 2aₙ₋₃ (since the sequence is not arithmetic or geometric, we can use this formula to find the nth term)
So, using this formula, we get:
a₂ = 3(32) - 2(-8) = 104
a₃ = 3(-8) - 2(2) = -26
And so on.
b)
a₁ = -7 (the first term of the sequence is given by the explicit formula)
aₙ = aₙ₋₁ + 10 (since the difference between consecutive terms is 10, we can use this formula to find the nth term recursively)
So, using this formula, we get:
a₂ = a₁ + 10 = 3
a₃ = a₂ + 10 = 13
And so on.
In general, the recursive formula for a sequence gives us a way to generate each term of the sequence based on the previous terms, while the explicit formula gives us a way to calculate any term of the sequence directly.
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Circle Theorems: How can you find the value of x?
Answer:
x = 52°
Step-by-step explanation:
Given various inscribed angles in a circle, you want the measure of central angle x.
Inscribed anglesThe inscribed angle theorem tells you an arc is double the measure of the inscribed angle it subtends:
arc JKM = 2·80° = 160°
arc JNL = 2·126° = 252°
Arcs of a circleThe sum of arcs around a circle is 360°. This tells you ...
arc JKL = 360° -252° = 108°
An arc has a measure equal to the sum of its parts, so ...
arc JKM = arc LM +arc JKL
160° = x + 108°
x = 52° . . . . . . . . . . subtract 108°
Dana invested $10,000 in a new technology stock. Six years later the stock had tripled in Value. What was the percent increase (rate of return) on her investment?
___________%
Answer:
The new value of the stock is 3 times the original value, which is $10,000 x 3 = $30,000.
The increase in value is $30,000 - $10,000 = $20,000.
The rate of return is the increase in value divided by the original investment, which is $20,000/$10,000 = 2 or 200%.
Therefore, the percent increase (rate of return) on Dana's investment is 200%.
Of the following, which best represents the graph of the region that corresponds to the inequalities 0 ≤ y ≤ 3 and x ≥ 0?
Is it Option 1 (all the way at the top), Option 2 (in the middle), or Option 3 (on the bottom)?
Or is it neither of them at all?
Option 1 is the correct answer.
Let's look at our constraint for the y value:
[tex]0\leq y\leq 3[/tex]. Remember that these are greater/lesser than or equal to symbols.
You can tell which way they're facing by what direction they open up in.
In this case, the first opens towards y, and the second opens towards 3.
This means that y is greater than or equal to 0, but lesser than or equal to 3.
This means that y, the vertical axis, can go from anywhere to 0 to 3.
Let's look at the constraint for the x value:
It's [tex]x\geq 0[/tex]. The sign is facing towards x, which means that x is greater than or equal to 0.
This means x (the horizontal axis) can range from 0 to positive infinity.
The y axis will not go above 3, and will not go below 0.
The x axis will not go below 0.
The only graph that satisfies these conditions is Option 1.
The y value does not go past 3, and does not go under 0.
The x value does not go to the left of 0, but goes on forever to the right.
local county officials have heard reports that a service station is allowing cars 20 years and older with known violations to pass their annual safety inspection. from administrative data, they know 30% of all cars 20 years and older do not pass their annual safety inspection. to test their theory about the service station, they request records from the most recent 150 inspections of cars of this type, finding 30 of the 150 had been rejected. let p be the true rate of cars 20 years and older that do not pass their annual safety inspection from this service station. what are the implied null and alternative hypotheses local county officials are testing?
The null hypothesis implied that cars 20 years or older do not pass safety inspection ≤ 30%.
The alternative hypothesis implied that cars 20 years or older do not pass safety inspection > 30%
The local county officials are testing a hypothesis about the proportion of cars 20 years.
And older that do not pass their annual safety inspection at the service station.
The null hypothesis and alternative hypothesis can be stated as follows,
Null hypothesis,
The true proportion of cars 20 years and older that do not pass their annual safety inspection at the service station ≤ 30%.
Alternative hypothesis,
The true proportion of cars 20 years and older that do not pass their annual safety inspection at the service station > 30%.
The null hypothesis assumes that the service station is not allowing cars with known violations to pass the safety inspection.
And that the rejection rate of 30% is consistent .
With the true rate of cars 20 years and older that do not pass their annual safety inspection at the service station.
The alternative hypothesis suggests that the service station is allowing cars with known violations to pass the safety inspection.
And that the rejection rate is lower than the true rate of cars 20 years .
And older that do not pass their annual safety inspection at the service station.
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Answer the question, if is correct I will give Brainliest
The bacterial culture loses half it's size every 0.167 seconds.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function in the context of this problem is defined as follows:
B(t) = 9300(1/64)^t.
The time needed for the population to lose half it's size is obtained as follows:
(1/64)^t = (1/2)
Considering the powers of two, in the denominator causing the negative signal, we have that:
2^(-6t) = 2^(-1)
6t = 1
t = 1/6
t = 0.167 seconds.
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Which expressions represent the distance between -5 and 3? Choose all that apply
Answer:
3-(-5)
Step-by-step explanation:
The distance between these two points is 8. And this is the only answer that acheives this sum.
Answer:
|-5 - 3|
|3 -(-5)|
Step-by-step explanation:
Point (-4, -5) is located in which quadrant?
Answer:
Quadrant 3.
Step-by-step explanation:
Quardant 1: Postive x-coordinate and postive y-coordinate. (northeast)
Quardant 2: Negative x-coordinate and postive y-coordinate. (northwest)
Quardant 3: Negative x-coordinate and negative y-coordinate. (southwest) <=
Quardant 4: Postive x-coordinate and negative y-coordinate. (southeast)
Therefore, it is the third one
