The dimensions of the wooden block are 14cm tall, 4cm long and 3 cm wide.
What is prism?In three dimensional space prism is a polyhedron where two ends are similar.
Given that volume of rectangular prism is 168 cubic centimeters.
And the wooden block is 2x cm tall, (x-4) cm wide and (x-3) cm long.
And also given that a wooden block in a set of building blocks is a rectangular prism.
That means,
Volume of wooden block = Volume of rectangular prism = 168 cm³
Volume of wooden block ;
length × width × height = 168 cm³
Substituting given values in above expression,
2x (x-3) (x-4) = 168 cm³
2x (x²-7x + 12) = 168 cm³
2x³ - 14x²+ 24x = 168 cm³
Simplifying the above equation;
2x³ - 14x²+ 24x- 168 = 0
x³ - 7x²+ 12x- 84 = 0
The factor of above cubic equation is x = 7.
Now the 2x = 14 , x-3 = 4, x-4 = 3.
Therefore the dimensions of the wooden block are 14cm tall, 4cm long and 3 cm wide.
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Name the property of a quality that justifies this statement
If m
A. Transitive property
B. Symmetric property
C. Reflexive property
D. Subtraction property
Subtraction property will satisfy given inequality option D.
Let's understand what is the Subtraction property
By balancing an equation with the same mathematical operation on both sides, the term "subtraction property of equality" is used.
Given inequality m< A + M <B = M<C. if we subtract both side equal value then we will get M<A = M<C - M<B. then we will get this result
or we can do cross-verify all other option
Transitive-According to the transitive property, "all the quantities are equal to each other if two quantities are equal to the third quantity."
Symmetric-Actually quite straightforward, equality has the symmetric property. According to this property, if a = b, then b must also be a. In other words, even if two equations' sides are switched, the.
Reflexive - It is said that a number is always equal to itself because of the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a. a=a.
So here we can see option D is most probable solution for given inequality.
Given Question is incomplete complete Question here
Name the Property of Equality that justifies the statement:
If m< A + M <B = M<C.
Then, M<A = M<C - M<B
Transitive Property
Symmetric Property
Reflexive Property
Subtraction Property
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64/8 I’m the simplest form
Answer:
8
Step-by-step explanation:
The first step would be to determine if both the numerator and the denominator have a highest common factor. If they do, then the number can be simplified into a smaller fraction. Here, the denominator can be fully divided out by 64 to make the whole number 8
What is the slope of the line that passes through (-5,6) and (-2,4)
The slope of the line that passes through the given points (-5, 6) and (-2, 4) as required in the task content is; -2 / 3.
What is the slope of the line that passes through the given points; (-5,6) and (-2,4)?It follows from the task content that the slope of the line that passes through the given points; (-5,6) and (-2,4) be determined as required.
On this note, since the slope, otherwise termed the average rate of change is given by the formula;
Slope, m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Therefore, given the points; (-5, 6) and (-2, 4), the required slope of the line is;
m = ( 4 - 6 ) / ( -2 - (-5) )
m = -2 / (-2 + 5)
m = -2 / 3
Therefore, the required slope of the line which passes through the given points is; -2 / 3.
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Edward did the following work to solve a system shown below. What does his answer mean?
Answer:
see explanation
Step-by-step explanation:
After solving a system of equations.
the solution is
36 = 32 ← not possible
the fact that we have 36 = 32, an impossible equation, means that the system has no solution.
the environmental protection agency (epa) rates the mean highway gas mileage of the 2013 ford edge to be 27 miles per gallon. assume the standard deviation is 3 miles per gallon. a rental car company buys 60 of these cars. what is the probability that the average mileage of the fleet is less than 26 miles per gallon?
the environmental protection agency (epa) rates the mean highway gas mileage of the 2013 ford edge to be 27 miles per gallon. assume the standard deviation is 3 miles per gallon. a rental car company buys 60 of these cars, 0.2979 is the probability that the average mileage of the fleet is less than 26 miles per gallon.
What is probability?Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A probability value between 0 and 1 represents an occurrence.
The four primary categories of probability are axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you might argue that it is the likelihood that a specific event will occur.
Given that,
μ = 27
σ = 3
n = 60
As we know,
= p ( 26 < x(avg.) < 26.8 )
= p (26 - 27 / 0.3873 ) < ( x(avg.) - μ(avg.)x /σx(avg.) ) < (26.8- 27/0.3873)
= p ( -1/ 0.3873 < z < -0.2 / 0.3873 )
= p ( -2.5820 < z < -0.5164 )
= p ( z < -0.5164) - p ( z < -2.5820 )
Using z table, we get -
= 0.3028- 0.0049
= 0.2979
Thus, probability = 0.2979
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If a film takes 90 minutes to show, what fraction of the film is completed 15 minutes after it begins? Show work.
Answer:
90-15=75
75/90= 5/6
ans: 5/6
1/6
Step-by-step explanation:Combine:We can combine the two numbers together to get the fraction we are looking for:
15/90
Simplify:By simplifying, we get:
1/6
We get this answer by dividing the highest possible number by both fractions. In this case, the number would be 15:
15 ÷ 15 = 1
90 ÷ 15 = 6
1/6
Solution:1/6
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
A coin is tossed and an equally divided spinner is spun. Cut in 5 containing numbers (1, 3, 5, 7, 9).
What is the probability of a head on the coin or a prime number on the spinner?
Explain Why
For the cards shown below what is the probability of choosing yellow card and then a 1 if the first card is replaced before the second card is drawn?
The study of probability is a field of mathematics that focuses on determining the possibility that an event will occur.
Describe probability..?"Finding the likelihood of the occurrence of an event" is the focus of the mathematical discipline known as probability.Formula of the probability of an event A is: [tex]P(A) = \frac{n(A)}{n(S)}[/tex]where [tex]n(A)[/tex] is the number of favorable outcomes[tex]n(S)[/tex] is the total number of events in the sample space.Given: a deck of cards with 2 red cards and 3 yellow cardsTotal cards = 5First we find the probability of choosing red cards.The probability of choosing one red card is 2/5.To learn more about probability refer to:
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The radius of a circle is 2 meters. What is the circle's area? r=2 m
3.14
The area of the circle with the given radius would be = 12.56m².
What is a circle?A circle is defined as the figure that do not posses any form of edges or corners and is known as a two dimensional figure with a center of 360°.
The area of the circle can be gotten when the radius is given.
The formula used for the calculation of the area of a circle = πr²
Where,
Pie (π) = 3.14 or 22/7
Radius (r) = 2 m
Area = 3.14 × 2²
= 3.14 ×4
= 12.56 m²
Therefore, the area of the given circle would be = 12.56m².
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solve for m,n, and p.
The measure of angle n is 73°, the measure of angle m is 51° and the line p measures 24 cm.
What is midpoint theorem?The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the length of the third side.
From the given figure, n is the midpoint of one side of the quadrilateral and m is the midpoint of other side of the quadrilateral.
Pair of opposite sides are parallel
Since, m and n are midpoints on two sides of quadrilateral, so the line passes through the midpoints is parallel to other two sides
Then, ∠n =73° and ∠m =51°
p = 1/2 ×48
⇒ p =24 cm
Therefore, the length of line p is 24 cm.
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Given \qquad m \angle ABDm∠ABDm, angle, A, B, D is a straight angle. \qquad m \angle CBD = 8x + 16^\circm∠CBD=8x+16 ∘ m, angle, C, B, D, equals, 8, x, plus, 16, degrees \qquad m \angle ABC = 6x - 60^\circm∠ABC=6x−60 ∘ m, angle, A, B, C, equals, 6, x, minus, 60, degrees Find m\angle ABCm∠ABCm, angle, A, B, C:
The value of measure m∠ABC will be 24°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
As per the given m∠ABD is a straight angle.
m∠ABD = 180°
m∠ABC + m∠CBD = m∠ABD
6x - 60 + 8x + 16 = 180°
14x - 44 = 180
14x = 224
x = 14
Thus, m∠ABC = 6(14) - 60 = 24°
Hence "Measure ∠ABC will equal 24° in value".
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The correct question below,
Your parents are saving up for a fun vacation at Disney. They have figured out it will
cost them a total of $3,400. If they already have $1,500 and plan on saving for the next
6 months, how much will they need to save each month to have at least enough money for
the trip? Write and solve an inequalit. Interpret your solution in sentence form.
A total of $316.67 has to be saved per month for the vacation at Disney.
What is equation modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.
Given is that your parents are saving up for a fun vacation at Disney. They have figured out it will cost them a total of $3,400. They have already saved $1,500 and plan on saving for the next 6 months,
Assume that they will have to save $x every month. So we can write the inequality as -
6x ≥ (3400 - 1500)
6x ≥ 1900
x ≥ (1900/6)
x ≥ 316.67
Therefore, your parents will have to save a total of $316.67 per month for the vacation.
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What is the product of 6/sqrt(3) and 3/sqrt(6) in simplest radical form?
The answer is 54√2.
What is simplest radical form?
The radical form is fairly simple. It refers to the form of numbers or algebraic expressions below radicals. However, this can be improved by manipulating numbers or algebraic expressions in their radical form into what is called the simplest radical form. There are no longer any square, cube, fourth, or other roots to be found when a radical is simplified into its simplest possible form. It also entails eliminating any radicals from the fraction's denominator.
SSolving the equations,
=6√3 × 3√6
=( 6 × 3 )√( 6 × 3 )
=18√18
= 18√(2×9)
=18 ( √2 × √9 )
=(18 × 3)√2
= 54√2
Therefore, The answer is 54√2.
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HELP!! Find (ƒ – g)(x) if f(x) = 4x² – 5x and g(x) = 3x² + 6x − 4.
-
○ (ƒ − g)(x) = −x² + 11x − 4
○ (ƒ − g)(x) = −x² — x^4
○ (ƒ − g)(x) = 7x² + x − 4
○ (ƒ − g)(x) = x² − 11x +4
○ (ƒ − g)(x) = x² − 11x +4 is the correct Answer
Answer:
ƒ(x) = 4x² – 5
g(x) = 3x² + 6x − 4.
(ƒ – g)(x) = ƒ(x)–g(x)
= 4x² – 5 –(3x² + 6x − 4)
= 4x²–5x –3x²–6x+4
= 4x²–3x² –5x–6x +4
= x² − 11x +4
[tex] [/tex]
Thank you
2, 10, 18,...
Find the 31st term.
Select the correct answer. What would be the value of $150 after eight years if you earn 12 percent interest per year? a. $371. 39 b. $415. 96 c. $465. 88.
The value will be $371.39.
What is compound interest?Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.
The formula to calculate the compound amount after t years is given by :-
A =P [tex](1 + R)^{T}[/tex]
where the interest rate is r and P represents the principal amount.
Given: $150 is the principal sum.
Interest is charged at a rate of 12%/0.12
A = 150 will be the amount compounded after 8 years.
A = 150 [tex]( 1 + 12 )^{8}[/tex]
A =371.3944
A = $371.39
Hence, the value of $150 after eight years if you earn 12 percent interest per year would be $371.39.
option a. is right
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X is a normally distributed random variable with mean 61 and standard deviation 8.
What is the probability that X is greater than 53?
The probability that X is greater than 53
What is probability ?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Formula for calculating the standard score or z score:
z = x-μ/σ, where:
z is the standard score
x is the raw score
μ is the population mean
σ is the population standard deviation
In this question: μ = 61 and σ = 8
The score is greater than 53
Let’s calculate the z score, for x = 53 and then find the probability for x greater than 53
z = (53 - 61)/8
= -8 / 8
= -1
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Find (2) (-3)
Help, help , help , help
Answer:
-6
Step-by-step explanation:
-6
Horn lengths of Texas longhorn cattle are normally distributed. The mean horn spread is 60 inches with a
standard deviation of 4.5 inches.
Calculate the range of horn lengths for the middle 95% of Texas Longhorn cattle. Show your work or
explain how you got your answer.
The range of horn lengths for the middle 95% of Texas Longhorn cattle is (51 inches, 69 inches)
What is a normal distribution?
A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.
Here, we have
Given:
Horn lengths of texas longhorn cattle are normally distributed
The mean horn spread: μ = 60 inches
With a standard deviation: σ = 4.5 inches
According to the normal distribution, the range for the middle 95% of the values is: (μ - 2σ, μ + 2σ)
Replacing the given values:
(60 inches - 2(4.5 inches), 60 inches + 2(4.5 inches))
(60 inches - 9 inches, 60 inches + 9 inches)
(51 inches, 69 inches)
Hence, the range of horn lengths for the middle 95% of Texas Longhorn cattle is (51 inches, 69 inches)
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The slope of a line is the rate of change in the y-coordinates (rise) to the corresponding change in the x-coordinates (run) for points on the line.
True false question.
True
False
Answer: True
Step-by-step explanation:
The slope is the rate of change, to find it, you can get rise/run or use the equation y2 - y1 / x2 - x1
So it is true!
what is the answer of this question?
Answer:208
Step-by-step explanation:
204+206+208.
Step-by-step explanation:
let the even numbers be :
x+(2+x)+(4+x)
so 3x+6=618
3x=618-6
3x/3=612/3
x=204
Find the simple interest:
Principal: $1,750
Interest Rate: 2%
Time: 9 years
an area of 10 square inches. Estimate the value to five decimal places.
Answer: sqrt 10
Step-by-step explanation:
3.16227...
elves really love candy canes. they eat 2 a day how many candy canes do they eat throughout the entire year
What is the coefficient in this expression? 25pq Responses 25 2/5 p p 5 5 2
The coefficient in the expression is 25.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.Given is the following expression -
f(p, q) = 25pq
The coefficient in the expression is 25.
Therefore, the coefficient in the expression is 25.
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Answer:
25
Step-by-step explanation:
While Zihao was pooping, Zihao-2 ringed to the door. Find the speed of Zihao to open the door, when toilet is on 25 m in front of the door for 5 sec
The speed of Zihao to open the door, when toilet is on 25 m in front of the door for 5 sec is 5m/sec.
What is meant by speed, distance and time?The formula used to explain the relationship between speed, distance, and time is speed distance time. That is speed = distance time. Alternatively, you can calculate the time by dividing the distance traveled by the speed. You can figure out the third input if you know two of the inputs. For instance, the length of the line segment that connects two points equals the distance between them. The formula for finding the distance between two points in a two-dimensional plane—which can be expanded to discover the distance between two points in a three-dimensional plane as well—is derived using the Pythagoras theorem.
Given,
Distance=25m
Time=5sec
Speed?
We know that,
Speed=Distance/Time
Speed=25/5
Speed=5m/sec
Therefore, the speed of Zihao to open the door, when toilet is on 25 m in front of the door for 5 sec is 5m/sec.
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what is the product of 73 and 4.4 x 10^6 expressed in scientific notation
Answer:
321.2 * 10^6
Step-by-step explanation:
First at all:
4.4 x 10^6 = 4.400.000
Then 73 * (4,4 x 10^6) = 73* 4.400.000
(73)*(4.400.000) = 321.200.000
In scientific notation:
321.2 * 10^6
What is the rate of 640:4
Answer: 160
Step-by-step explanation: If I remember correctly, the formula for finding the rate is:
r = d/t
So, rate = 640/4
When I divided it, I got 160.
I hope this helped!
Answer:
25.6
Step-by-step explanation:
while i do not know how to do this is dod use a rate calculator so hopes this help!
What is 3 percent of 98
Answer:
2.94
Step-by-step explanation:
I just found 1%
Which is 0.98
then times that by 3 which is 2.94
hope that helps!
What is the product of 9 and 8√90 in simplest radical form?
Simplest Radical Form of the given question is [tex]216\sqrt{10}[/tex].
What is a Radical?An phrase that has a root, typically a square or cube root, is referred to as a radical.
The radical consists of three separate parts:
Radicand :This is the one whose root you are discovering.
A radical equation is one that contains the square root, or at least one other variable expression, inside a radical.
Degree: It expresses the degree of radicand multiplication. If a number appears on the root symbol but is absent, it is taken to be 2. (square root).
Symbol: Usually √
Calculation:Given
[tex]9,8\sqrt{90}\\ 9*8\sqrt{90}=9*8\sqrt{9*10}=9*8*3\sqrt{10} \\=216\sqrt{10}[/tex]
Simplest Radical Form of the given question is [tex]216\sqrt{10}[/tex].
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