The probability of escape for the guest is approximately 9 - √27/4.
This can be calculated using the principle of inclusion-exclusion. To calculate the probability of escape, we can calculate the probability of the guest being unable to move from Room 0 to any of the other rooms.
This is the probability of all doors from Room 0 being locked, which is equal to 1/3 x 1/3 = 1/9. Therefore, the probability of escape is 1 - 1/9 = 8/9.
Using the inclusion-exclusion principle, we can calculate the probability of the guest being able to move from Room 0 to any of the other rooms. The probability of the guest being able to move from Room 0 to any of the other rooms is equal to 1 - (1/3 + 1/3 - 1/9) = 9 - √27/4.
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Can someone answer this question for me? thank you
2 moles of Al is required to react with 213 g of Cl2.
What is the number of moles?The number of moles is a unit of measurement used in chemistry to express the amount of a substance. One mole (mol) of a substance contains Avogadro's number of particles, which is approximately 6.02 x 10^23 particles. The particles can be atoms, molecules, ions, electrons, or any other particles that make up a substance.
2Al + 3Cl2 -----> 2AlCl3
Number of moles of Cl2 = 213 g/71 g/mol
= 3 moles
If 2 moles of Al reacts with 3 moles of Cl2
x moles of Al reacts with 3 moles of Cl2
x = 2 * 3/3
= 2 moles
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how to find the % of any number?
Answer:
Divide the number by 100
Step-by-step explanation:
The percentage of a number is it's relation in terms of 100. So to get the percentage of a number you have to divide it by 100
e.g 10 is a number
10/100
That is 0.1%
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A microwave was originally sold for $148 and has been marked up to $222. What is the percentage increase for the microwave? Round to the nearest one percent.
Answer:
I think the answer is 33%
Answer:
33%
Step-by-step explanation:
the percent difference of 222 to 148 is 66.66. meaning 100%-66.66% is 33.34%. rounding this the the nearest one percent is 33%. the microwave price has increased by 33% respectively .
Mike constructed a kite by attaching two congruent triangles as shown in the diagram below. Which equation can Mike use to determine the amount of material, in square inches, needed to create the kite?
F. A=[12(12)(8)]⋅2
G.A=[12(6)(8)]⋅2
H.A=[(12)(4)]⋅2
J.A=[(6)(10)]⋅2
Answer: We cannot provide a complete answer as there is no diagram attached to the question. However, based on the information provided, we can make an educated guess as to which equation Mike can use to determine the amount of material, in square inches, needed to create the kite.
Since Mike constructed the kite by attaching two congruent triangles, we can use the formula for the area of a triangle, which is:
A = (1/2) * base * height
To find the area of both triangles, we need to know the base and height of each triangle. Without a diagram, we cannot determine the exact dimensions of the triangles.
However, based on the answer choices provided, we can make an assumption that the kite is made up of two congruent right triangles, each with legs of length 6 inches and 8 inches. Using this assumption, we can determine the area of each triangle and then multiply by 2 to get the total area of the kite.
Using the formula for the area of a triangle, we get:
A = (1/2) * base * height
= (1/2) * 6 * 8
= 24
So the area of each triangle is 24 square inches, and the total area of the kite is:
A = 2 * 24
= 48
Therefore, the equation that Mike can use to determine the amount of material, in square inches, needed to create the kite is likely to be:
G. A = [12(6)(8)]⋅2
This equation corresponds to the area of two congruent right triangles with legs of length 6 inches and 8 inches.
Step-by-step explanation:
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
A. 14 and 1 over 7 in2
B. 23 and 4 over 7 in2
C. 47 and 1 over 7 in2
D. 84 and 6 over 7 in2
Answer:
D. 84 and 6 over 7 in2
Step-by-step explanation:
The surface area of the cylindrical mini muffin can be calculated as follows:
Surface area = 2πr^2 + 2πrh
where r is the radius of the circular base and h is the height of the cylinder.
Given that the diameter of the mini muffin is 2 inches, the radius can be calculated as 1 inch (since radius = diameter / 2).
So, r = 1 inch and h = 1 and 1/4 inches.
Substituting these values into the surface area formula, we get:
Surface area = 2 x (22/7) x 1^2 + 2 x (22/7) x 1 x (5/4)
= (44/7) + (55/7)
= 99/7
≈ 14.14 square inches
Therefore, the surface area of 1 mini muffin is approximately 14.14 square inches.
To wrap 6 mini muffins, we need to multiply the surface area of 1 mini muffin by 6:
Surface area of 6 mini muffins = 6 x 14.14
≈ 84.84 square inches
Rounding off to one decimal place, the minimum amount of paper needed to wrap 6 mini muffins is approximately 84.8 square inches, which is closest to option D, 84 and 6/7 in^2.
Find the logistic function f with the given properties.
f(0) = 1, f has limiting value 11, and for small values of x, f is approximately exponential and grows by 75% with every increase of 1 in x.
f(x) = ____
The logistic function is then given by f(x) = 11 / (1 + e^(-0.75x))
The logistic function with the given properties is given by: f(x) = 11 / (1 + e^(-0.75x))
To understand this, we can start by noticing that for small values of x, f is approximately exponential and grows by 75% with every increase of 1 in x. This implies that the function can be written as f(x) = e^(0.75x). Since the limiting value of f is 11, the function can be written as f(x) = 11e^(0.75x). The logistic function is then given by f(x) = 11 / (1 + e^(-0.75x)), which satisfies the given conditions.
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Round your answer to the nearest hundredth.
A right triangle A B C. Angle A C B is a right angle. Angle B A C is unknown. Side A C is two units. Side A B is eight units.
The angle is [tex]m\angle{BAC}[/tex]=75.5°.
What is trigonometric function?The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
Here in the given right triangle ABC, [tex]m\angle{ACB}[/tex]=90° and AC = 2 units ,
AB = 8 units. We need to find angle BAC.
Using cosine ratio,
=> Cos BAC = [tex]\frac{adjacent}{hypotenuse} = \frac{AC}{AB}[/tex]
=> Cos BAC = [tex]\frac{2}{8}=\frac{1}{4}=0.25[/tex]
=> [tex]m\angle {BAC} = cos^{-1}(0.25)[/tex] = 75.5°
Hence the angle is [tex]m\angle{BAC}[/tex]=75.5°.
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Which point has coordinates (4.9, 3.9)?
Answer:
C
Step-by-step explanation:
Answer: c.
Step-by-step explanation:
HELP BRO MY BRAIN CELLS ARE DISSOLVING
Answer:
Step-by-step explanation:
(2x + 3) + (6x + 25) = 180 they are supplementary angles
8x + 28 = 180
8x = 180 - 28 = 252
x = 152/8 = 19
m∠EFG = 6x + 25 = 6(19) + 25 = 139
m∠IFH = 90 - (2x + 3) = 90 - 2(19) - 3 = 49
∠EFD≅∠GFH because they are vertical angles
Determine the domain of the quadratic function. f (x) = 7x2 - 10x + 10 Get Hint Enter Your Stop Here 16 8704 МАА 3
The domain of the quadratic function f(x) = 7x2 - 10x + 10 is all real numbers.
To determine the domain, set the equation equal to 0 and solve for x.
7x² - 10x + 10 = 0
7x2 - 10x = -10
7x(x - 10) = -10
x(x - 10) = -10/7
x = 10 or x = -10/7
The domain of a function is the set of all possible input values (x-values) for which the function is defined. In the case of the quadratic function f(x) = 7x^2 - 10x + 10, there are no restrictions on the values that x can take.
That is, any real number can be plugged in for x, and the function will give a real output. Therefore, the domain of this quadratic function is all real numbers, or (-∞, ∞).
Since there are no restrictions on x, the domain of the function is all real numbers.
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a 5.23. Exercise. Make a ruler-and-compass construction of the center of given circle.
The center of the circle can be found using a ruler-and-compass construction by drawing two arcs that intersect at the center of the circle. The radius of the circle can also be found using a ruler by measuring the distance from the center of the circle to any point on the circumference of the circle.
To make a ruler-and-compass construction of the center of a given circle, follow these steps:
Draw a line segment through the center of the circle using a ruler. This line segment should intersect the circle at two points.
Using a compass, draw an arc with the center at one of the intersection points and the radius equal to the length of the line segment.
Draw another arc with the center at the other intersection point and the same radius.
The point where the two arcs intersect is the center of the circle.
Use a ruler to draw a line from the center of the circle to any point on the circumference of the circle. This line is the radius of the circle.
The center of the circle can be found using a ruler-and-compass construction by drawing two arcs that intersect at the center of the circle. The radius of the circle can also be found using a ruler by measuring the distance from the center of the circle to any point on the circumference of the circle.
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a village contains contains n people a medical team inculates m people each day aginst yellow fever after foour days how many people still neeed to be inoculated
n-4m people still need to be inoculated. As the village contains n people and a medical team insulate m people each day against yellow fever.
It is given in the question that there is n number of people in the village.
Number of people inculcated each day against yellow fever = m
Now for finding how many people have been inculcated against yellow fever we will multiply by 4 the number of people who are being inculcated against yellow fever with m
So, in four days the number of people that had been inculcated is 4m
For finding how many people are left to be inculcated against yellow fever we will subtract from the total number of people in the village the number of people who have been inoculated against yellow fever
Therefore, People left after four days to be inculcated is = n-4m
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Given f (x) = |x| - 3; x ≥
0, write an equation for f -1(x).
(Hint: Sketch f (x) and note the domain
and range.)
Select one:
a. f -1(x) = |x + 3|;
x ≥ 0
b. f -1(x) = |x | + 3;
x ≥ -3
c. f -1(x)
The correct answer is option b. f -1(x) = |x| + 3; x ≥ -3.
To find the inverse of a function, we can switch the x and y values and solve for y. In this case, we can start with the original equation:
f(x) = |x| - 3
Switch the x and y values:
x = |y| - 3
Solve for y:
|x| = y + 3
|y| = x + 3
Since the original function has a domain of x ≥ 0, the inverse function will have a range of y ≥ 0. This means that the absolute value of y will always be positive, so we can drop the absolute value bars:
y = x + 3
So the inverse function is:
f -1(x) = x + 3
And since the original function has a domain of x ≥ 0, the inverse function will have a domain of x ≥ -3. So the final equation for the inverse function is: f -1(x) = x + 3; x ≥ -3
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Show that circle D with center open parentheses 8 comma negative 2 close parentheses and radius 8 is similar to circle E with center (5, 1) and radius 2.
The ratio of their radii is 8/2 = 4.
What is ratio?Ratio is a comparison of two or more quantities expressed in terms of their relative sizes. It is a way to express one number as a fraction of another number. For example, if a person has three apples and two oranges, the ratio of apples to oranges can be expressed as 3:2. Ratios can also be expressed as fractions or percentages.
To show that Circle D and Circle E are similar, we need to determine if the ratio of their radii is equal to the ratio of their distances from the origin. The ratio of their radii is 8/2 = 4. The distance from the origin for Circle D is sqrt((8)²+ (-2)²) = sqrt(64 + 4) = sqrt(68) = 8.24. For Circle E, the distance from the origin is sqrt((5)² + (1)²) = sqrt(26) = 5.1. The ratio of their distances from the origin is 8.24/5.1 = 1.61. Since the ratio of their radii (4) is equal to the ratio of their distances from the origin (1.61), we can conclude that Circle D and Circle E are similar.
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6. Over this same am interval we also have probe permeameter measurements These are plotted vs depth and displayed for comparison with the core plugs Can you see the pericability (geological structure more clearly? Given the following analysis of the probe data can we expect an average within 20% of the arithmetic average? What is the true beterogeneity level of this interval and what do you think controls it? What are the implications for the grid block permeabilities? Department of Petroleum Engineering. Hunor Wall Undersey 29 EUM. SCIENCE Probe permeability 320 151 93 No. of meas, Arith. av. (m) Geom. av. (mD) Harm av. (D) CV No Vdp 39 0.82 0.69
Based on the given data, it is difficult to see the permeability or geological structure more clearly from the probe permeameter measurements compared to the core plugs.
It is unlikely that we can expect an average within 20% of the arithmetic average, given the high level of heterogeneity and wide range of permeability values.
The implications for the grid block permeabilities are that there may be significant variability within the grid blocks
The probe data shows a wide range of permeability values, ranging from 320 mD to 93 mD, with an arithmetic average of 151 mD, geometric average of 0.82 mD, and harmonic average of 0.69 mD. The coefficient of variation (CV) is also quite high at 39, indicating a high level of heterogeneity within the interval.
It is unlikely that we can expect an average within 20% of the arithmetic average, given the high level of heterogeneity and wide range of permeability values. The true heterogeneity level of this interval is likely to be quite high, as indicated by the high CV value.
The controls on the heterogeneity level of this interval could be related to the geological structure and lithology of the reservoir, as well as the presence of fractures or faults. These factors can all impact the permeability and flow of fluids within the reservoir.
The implications for the grid block permeabilities are that there may be significant variability within the grid blocks, and this could impact the flow of fluids and the overall production from the reservoir. It may be necessary to use more detailed modeling techniques to accurately capture the heterogeneity within the grid blocks and better predict the flow of fluids within the reservoir.
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Introduction to the LCM of two monomial Find the least common multiple of 6x^(3) and 8n^(4).
This is the least common multiple of 6x3 and 8n4. The least common multiple (LCM) of two monomials is the lowest common multiple of the coefficients and the highest sum of exponents for each variable.
To find the LCM of 6x3 and 8n4, we need to find the highest sum of exponents for each variable (in this case, 3 for x and 4 for n). Then, multiply the coefficients together to get 48x3n4. This is the least common multiple of 6x3 and 8n4.
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I need some help please
The solution to the given inequality |3x + 4| > 6 is x < -10/3 or x > 2/3
How to solve inequality?Inequality is a statement that is of two quantities in which one is specifically less than (or greater than) another. The symbols of inequality includes;
Greater than >
Less than <
Equal to =
Greater than or equal to ≥
Less than or equal to ≤
|3x + 4| > 6
First case:
+(3x + 4) > 6
3x + 4 > 6
subtract 4 from both sides
3x > 6 - 4
3x > 2
divide both sides by 3
x > 2/3
Second case:
-(3x + 4) > 6
-3x - 4 > 6
Add 4 to both sides
-3x > 6 + 4
-3x > 10
x < 10/-3
Hence, x < -10/3 or x > 2/3
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4. Prove/disprove: (a) The functionT:Rn→Rdefined byT(v)=∥v∥is a linear transformation. (b) Letx∈Rnbe a fixed vector. The functionT:Rn→Rdefined byT(v)=v⋅xis a linear transformation. (c) LetA∈Mn×n(F)be an invertible matrix, and letTA:Fn→Fnbe the linear transformation determined byA. For ally∈Fn, there exists a uniquex∈Fnsuch thatTA(x)=y(d) LetA,B∈Mn×n(F). Suppose thatAB=ATand thatAis invertible. ThenBmust be invertible.
a)T(v)=∥v∥ is not a linear transformation.
b)T(v)=v⋅x is a linear transformation.
c)TA(x)=y.
d)B must also be invertible.
a) The function T:Rn→R defined by T(v)=∥v∥ is not a linear transformation.
b) The function T:Rn→R defined by T(v)=v⋅x is a linear transformation.
c) Let A∈Mnxn(F) be an invertible matrix, and let TA:Fn→Fn be the linear transformation determined by A. For all y∈Fn, there exists a unique x∈Fn such that TA(x)=y.
d) Let A,B∈Mnxn(F). Suppose that AB=AT and that A is invertible. Then B must also be invertible.
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Which function represents exponential decay?
A. f(x) = 0.25(1.06)
B. f(x) = 18 +0.9x
c. f(x) = 412 + 1.03x
D. f(x) = 268(0.86)*
Answer: The function that represents exponential decay is:
D. f(x) = 268(0.86)^x
This function has a base of 0.86, which is less than 1. As x increases, the value of the function decreases exponentially. This is the characteristic of exponential decay, where the value of a quantity decreases at a constant percentage rate over time.
Option A, f(x) = 0.25(1.06), represents exponential growth, as the base (1.06) is greater than 1.
Option B, f(x) = 18 + 0.9x, represents linear growth, as the value of the function increases linearly with x.
Option C, f(x) = 412 + 1.03x, also represents linear growth, as the value of the function increases linearly with x.
Step-by-step explanation:
The following list shows the number of new memberships that a gym has sold each day over the past week: 4, 2, 9, 2, 0, 3, 8. Which of the following is not a true statement?
Show quoted text
The median of the data is 2 is not a true statement. (second option).
What is the median?Mean is the average of a set of numbers.
Mean = sum of numbers / total numbers
(0 + 2 + 2 + 3 + 4 + 8 + 9) / 7 = 28 / 7 = 4
Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order.
The numbers in ascending order is: 0, 2, 2, 3, 4, 8, 9
Median = 3
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Hi. _______________________________________________________________________________
Answer:
.
Step-by-step explanation:
I need help writing equations of a parallel and perpendicular equations
The equation of the line that is parallel to y = 2/5x + 2 and passes through (-5, 6) is y = (2/5)x + 8.
What connection exists between the slopes of parallel and perpendicular lines?Perpendicular line slopes are the negative reciprocals of one another. In other words, any line that is perpendicular to a line with a slope of m will have a slope of -1/m. If lines are parallel if they have the same slope.
The slope of the given line is 2/5.
We know that, any line perpendicular to it will have a slope that is the negative reciprocal of 2/5, which is -5/2.
Using the point-slope form of a line:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Substituting the values we know:
y - 6 = (-5/2)(x - (-5))
y - 6 = (-5/2)x - (25/2)
y = (-5/2)x + 17.5
Therefore, the equation of the line perpendicular to y = 2/5x + 2 and passes through (-5, 6) is y = (-5/2)x + 17.5.
The slope of parallel lines are same. Thus, using point slope form:
y - 6 = (2/5)(x - (-5))
y - 6 = (2/5)x + 2
y = (2/5)x + 8
Therefore, the equation of the line that is parallel to y = 2/5x + 2 and passes through (-5, 6) is y = (2/5)x + 8.
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A data firm records large amount of data. Historically, .9% of the pages of data recorded by the firm contain errors If 200 pages of data are randomly selected, What is the probability that six or more pages contain errors? b What is the probability that more than 10 pages contain errors? What is the probability that none ofthe pages contain errors? d. What is the probability that fewer than five pages contain errors?
There is a 0.0876 percent probability that six or more pages will include mistakes. There is a 1.64 x 10⁻⁶ chance that more than 10 pages may include mistakes.
What purposes does probability serve?Information about possibility of occurrence is provided by probability. For instance, weather patterns are used by meteorologists to predict the possibility of rain. In order to understand the relationship between exposures and the risk of health outcomes, epidemiology uses probability theory.
a) Chance that six or more pages may have mistakes:
To get this probability, we can utilise the binomial probability formula:
P(X>=6) = 1-P(X<6)
where X is the number of pages with errors.
P(X<6) = P(X=0)+P(X=1)+P(X=2) +P(X=3)+P(X=4)+P(X=5)
For each term, using the binomial probability formula, we obtain:
P(X < 6) = 0.9124
Therefore, P(X >= 6) = 1 - P(X < 6) = 1 - 0.9124 = 0.0876
Hence, there is a 0.0876 percent chance that six or more pages will include errors.
b) Chance that there are errors on more than 10 pages:
Using the same method, we can discover:
P(X > 10) = P(X = 11) + P(X = 12) + ... + P(X = 200)
To find the likelihood, we can use a calculator or software because performing the math by hand can be very time-consuming. Using a calculator for the binomial distribution, we obtain:
P(X > 10) = 1.64 x 10⁻⁶ (rounded to 3 decimal places)
Hence, there is a roughly 10% chance that there will be errors on more than 10 pages. 1.64 x 10⁻⁶.
c) Probability that none of the pages contain errors:
P(X = 0) can be calculated using the binomial probability formula:
P(X = 0) = (200 choose 0) * (0.009)⁰ * (1 - 0.009)²⁰⁰
= 0.8196
As a result, 0.8196 percent of the pages are likely to be error-free.
d) Probability that fewer than five pages contain errors:
P(X<5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
Again, using the binomial probability formula for each term, we get:
P(X < 5) = 0.8151
Hence, the likelihood that fewer than five pages are mistake-free is 0.8151.
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a right rectangular prism shown is made up of 24 cubes . each cube has an edge length of 3/4 cubic inch what is the volume of this prism
Answer:
To find the volume of the right rectangular prism, we need to know its dimensions, which we can determine from the number of cubes it's made up of. Since the prism is made up of 24 cubes and each cube has an edge length of 3/4 cubic inch, we can find the dimensions of the prism as follows:
The number of cubes along the length of the prism is equal to the number of cubes along one of its edges. Since the edge length of each cube is 3/4 cubic inch, we can find the number of cubes along the length of the prism by dividing the total length of the prism by the edge length of each cube:
Number of cubes along the length = Total length / Edge length of each cube
= 24 cubes x (3/4) inch/cube
= 18 inches
Similarly, we can find the number of cubes along the width and height of the prism:
Number of cubes along the width = 24 cubes x (3/4) inch/cube = 12 inches
Number of cubes along the height = 24 cubes x (3/4) inch/cube = 8 inches
Now that we know the dimensions of the prism, we can find its volume by multiplying its length, width, and height:
Volume of the prism = Length x Width x Height
= 18 inches x 12 inches x 8 inches
= 1728 cubic inches
Therefore, the volume of the right rectangular prism is 1728 cubic inches.
Step-by-step explanation:
explanation of how to find the volume of the right rectangular prism made up of 24 cubes:
Given: The prism is made up of 24 cubes, and each cube has an edge length of 3/4 cubic inch.
To find the dimensions of the prism, we need to determine the number of cubes along each edge of the prism. Since the prism is made up of 24 cubes, we can divide the total number of cubes by the number of cubes along one of its edges to find the length of each edge:
Length of each edge = Total number of cubes^(1/3)
= 24^(1/3)
= 2.88 (rounded to two decimal places)
Now that we know the length of each edge of the prism, we can find its dimensions by multiplying the length of each edge by the edge length of each cube:
Length of the prism = 2.88 x 3/4 = 2.16 inches
Width of the prism = 2.88 x 3/4 = 2.16 inches
Height of the prism = 2.88 x 3/4 = 2.16 inches
Finally, we can find the volume of the prism by multiplying its length, width, and height:
Volume of the prism = Length x Width x Height
= 2.16 inches x 2.16 inches x 2.16 inches
= 10.79 cubic inches (rounded to two decimal places)
Therefore, the volume of the right rectangular prism made up of 24 cubes is 10.79 cubic inches.
The volume of the right rectangular prism is 27/2 cubic inches, and explains how that value was obtained from the given information.
How to find the volume of the rectangular prism?Since the rectangular prism is made up of 24 cubes, we can find its volume by multiplying the number of cubes by the volume of each cube.
The edge length of each cube is 3/4 cubic inch, so the volume of each cube is:
(3/4)³ = 27/64 cubic inches.
Therefore, the volume of the rectangular prism is:
24 x (27/64) = (24 x 27)/(4 x 4 x 4) = 27/2 cubic inches.
So the volume of the rectangular prism is 27/2 cubic inches.
We are given that the right rectangular prism is made up of 24 cubes, and that each cube has an edge length of 3/4 cubic inch. We want to find the volume of the prism.
Find the volume of each cube:
The volume of a cube is given by V = s³, where s is the length of an edge. In this case, we are given that the length of an edge is 3/4 cubic inch, so we can substitute that value into the formula:
V = (3/4)³
V = 27/64 cubic inches
So the volume of each cube is 27/64 cubic inches.
Find the volume of the rectangular prism:
To find the volume of the rectangular prism, we need to multiply the number of cubes by the volume of each cube. We know that there are 24 cubes, so we can substitute that value into the formula:
Volume of prism = number of cubes x volume of each cube
Volume of prism = 24 x (27/64)
Volume of prism = (24 x 27)/(4 x 4 x 4)
Volume of prism = 27/2 cubic inches
So the volume of the rectangular prism is 27/2 cubic inches.
Therefore, the volume of the right rectangular prism is 27/2 cubic inches, and explains how that value was obtained from the given information.
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Find the fourth term of an arithmetic sequence with a_(1)=3 and a recursive formula of a_(n)=a_(n-1)-9.
The fourth term of the arithmetic sequence is -24.
What is arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term after the first is formed by adding a constant, called the common difference, to the preceding term.
The fourth term of an arithmetic sequence with a1=3 and a recursive formula of an=an-1-9 can be found by using the recursive formula repeatedly until the fourth term is reached.
First, find the second term by plugging in n=2 into the recursive formula:
a2=a2-1-9=a1-9=3-9=-6
Next, find the third term by plugging in n=3:
a3=a3-1-9=a2-9=-6-9=-15
Finally, find the fourth term by plugging in n=4:
a4=a4-1-9=a3-9=-15-9=-24
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x^2+14x-51=0 I have solve by completing the square
Answer:
x=3 or x=−17
Step-by-step explanation:
Let's solve your equation step-by-step.
x2+14x−51=0
Step 1: Add 51 to both sides.
x2+14x−51+51=0+51
x2+14x=51
Step 2: The coefficient of 14x is 14. Let b=14.
Then we need to add (b/2)^2=49 to both sides to complete the square.
Add 49 to both sides.
x2+14x+49=51+49
x2+14x+49=100
Step 3: Factor left side.
(x+7)2=100
Step 4: Take square root.
x+7=±√100
Step 5: Add -7 to both sides.
x+7+−7=−7±√100
x=−7±√100
x=−7+10 or x=−7−10
x=3 or x=−17
A toy shop purchases 125 identical stuffed animals for a total cost of $312.50 and sells them for $7 each. What is the percent markup?
Answer:
180%
Step-by-step explanation:
Were given the total cost for all the stuffies, and the individual sale price for the stuffies, to convert them in all individual price divide 312.5 by 125 which equals 2.5. to find percent markup do (selling price - unit cost)/unit cost. Then multiply to get percentage. Therefore (7-2.5)/2.5=1.8. 1.8*100 = 180% markup
To operate safely the total weight on an elevator must be less than 400 pounds
The inequality of the statement is x < 400
How to determine the inequality of the statementFrom the question, we have the following parameters that can be used in our computation:
To operate safely the total weight on an elevator must be less than 400 pounds
Represent the variable with x
So, we have
x must be less than 400 pounds
less than can be represented as <
Using the above as a guide, we have the following:
x < 400
Hence, the expression is x < 400
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(3)/(x^(2)-2x-8)-(4)/(x^(2)-16) Simplify. Assume that all variables result in nonzero denominators.
The simplified expression is (-1)/((x+2)(x+4)).
To simplify the expression (3)/(x^(2)-2x-8)-(4)/(x^(2)-16), we need to find a common denominator and combine the numerators.
Factor the denominators to find a common denominator.
(x^(2)-2x-8) = (x-4)(x+2)
(x^(2)-16) = (x-4)(x+4)
The common denominator is (x-4)(x+2)(x+4).
Multiply the numerators and denominators by the appropriate factors to get the common denominator.
(3)/(x^(2)-2x-8) = (3)(x+4)/((x-4)(x+2)(x+4))
(4)/(x^(2)-16) = (4)(x+2)/((x-4)(x+2)(x+4))
Combine the numerators and keep the common denominator.
(3)(x+4)/((x-4)(x+2)(x+4)) - (4)(x+2)/((x-4)(x+2)(x+4)) = (3x+12-4x-8)/((x-4)(x+2)(x+4))
Simplify the numerator and denominator.
(-x+4)/((x-4)(x+2)(x+4)) = (-1)(x-4)/((x-4)(x+2)(x+4))
Cancel out the common factors in the numerator and denominator.
(-1)/((x+2)(x+4))
Therefore, the simplified expression is (-1)/((x+2)(x+4)).
Note: We assumed that all variables result in nonzero denominators, so we do not need to worry about any restrictions on the values of x.
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in the diagram ehat is the ratio of patterend circles to plain circles
Answer:5:7
Step-by-step explanation:
From the given graph it is clear that
The total number of circles = 12
The total number of patterned circles = 5
The total number of plain circles = 7
We need to find the ratio of patterned circles to plain circles.
Substitute patterned circles = 5 and plain circles = 7 in the above formula.
Therefore, the ratio of patterned circles to plain circles is 5:7.