The volume of solid B is 1350 [tex]cm^{3}[/tex].
What is the volume ratio?
The side length ratio raised to the third power represents the volume ratio for the two solids.
If two solids are comparable, their volumes will have a ratio that is equal to the cube of their corresponding side ratios.
Given that both solids are similar.
The volume of solid A = 400 [tex]cm^{3}[/tex]
height of solid A = 10 cm
height of solid B = 15 cm
the volume of solid B = ?
Now,
volume of solid A/ volume of solid B = (height of solid A)^3/(height of solid B)^3
or, [tex]\frac{400}{x} = \frac{10^{3} }{15^{3} }[/tex]
or, [tex]x = \frac{400*15^{3} }{10^{3}}[/tex]
or, [tex]x = \frac{400*3375 }{1000}[/tex] = 1350
Hence, the volume of solid B is 1350 [tex]cm^{3}[/tex].
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The graph states f(x) is at(4,3) and g(x) is at (4,3) what input value produces the same output value for the two functions on the graph?
The ordered pair of the values of f(x) and g(x) of (4, 3) and (4, 3) indicates that the input value that produces the same output value for f(x) and g(x) functions is x = 3
What are the input and output values of a function?The input values of a function are the values that serve as the argument of the function. They are also known as the independent variable. The operations of a function are performed on the input values such that each input produces only one output, which is known as the dependent variable. The set of the input values is known as the domain of the function.
The output value of a function are the values of the function that gives the image of the input values, and they are known as the dependent variable. The set of the output values is the range of the function.
The points on the graph are;
f(x) = (4, 3), and g(x) = (4, 3)Therefore, from the graph, at the point x = 3, f(x) = g(x) = 4
The input value that produces the same output value for the two functions on the graph is the x-value of 3
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Linda has a shelf that is 56 over 5 inches wide. How many catalogs can Linda arrange on the shelf if each catalog is 4 over 5 of an inch thick?
Answer:
Last option: 31
Step-by-step explanation:
No. of catalogs that can be arranged
= (longest side of shelf ÷ longest side of catalog) × (shortest side of shelf ÷ shortest side of catalog)
= (56 ÷ 5) × (5 ÷ 4)
= 31
A midwife delivers 10 babies considering a % chance of delivering a boy and 50% chance of delivering a girl, answer the following questions what is the probability that 6 of the babies will be boys?
A midwife delivers 10 babies, with 50% chance of delivering a boy and 50% of delivering a girl. The probability that 6 out of 10 babies will be boys is 20.5%
The problem can be solved using binomial distribution, that is the probability of 2 possible outcomes in a number of trials.
The formula is given by:
P(x) = ⁿCx . P^x . (1 - P)^(n-x)
x = total number of event A
n = number of trials
P = probability of A in a single trial
Parameters given in the problem:
n = 10
x = 6
P = 50% = 0.5
Plug these parameters into the formula:
P(6 boys) = ¹⁰C₆ . (0.5)⁶ . (0.5)⁴
= 0.205 = 20.5%
Hence, the probability that 6 out of 10 babies will be boys is 20.5%
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factorise 2x^[2]-9x-5
Answer:
(2x + 1) and (x - 5)
Step-by-step explanation:
(2x + 1)(x - 5) = 2x^2 - 9x - 5
Given the function below, find value (a) of x if f(x)=7
The function f(x) = 2x + 1 has its value of x to be 3 when f(x) = 7
How to determine the value of the function?From the possible question, the definition of the function is given as
f(x) = 2x + 1
Also, from the question, we have:
f(x) = 7
Substitute 7 for x in the equation f(x) = 2x + 1
So, we have the following representation
2x + 1 = 7
Subtract 1 from both sides of the equation
This gives
2x = 6
Divide both sides by 2
x = 3
So, we can conclude that the value of x is 3
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Possible question
Given the function below, find the value of x if f(x)=7
f(x) = 2x + 1
a group contains n men and n women. identify the steps used to find the number of ways to arrange n men and n women in a row if the men and women alternate?
With the help of factorisation we can conclude our answer.
What is factorisation?The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into the product of another entity, or factors, whose multiplication results in the original number or matrix is known as factorization or factoring in mathematics.A polynomial or integer is simply resolved into components that, when multiplied together, produce the original or starting polynomial or integer. The factorization method allows us to simplify any algebraic or quadratic equation by representing the equations as the product of factors rather than by expanding the brackets. Any equation can have an integer, a variable, or the algebraic expression itself as a factor.acc to our question-
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Can someone please explain to me in simple words how to construct the circumcenter and incenter of a triangle? I've tried watching videos and reading articles but the wording is too complicated.
I'm doing the IXL skill if that helps
The circumcenter is where three perpendicular bisectors intersect and the incenter is where the three angle bisectors intersect.
What is circumcenter?The circumscribed circle or circumcircle of a polygon in geometry is a circle that passes through each of the polygon's vertices. This circle's circumcenter and circumradius are its centre and radius, respectively.
Construct angle bisectors of each angle of the triangle and their intersection point gives the incenter.
To find Circumcenter:
Construct perpendicular bisectors of all sides of the triangle and their intersection point gives the circumcenter.
Circumcenter Theorem: It states that the vertices of a triangle are equidistant from the circumcenter.
Incenter Theorem: It states that the incenter is equidistant from the sides of the triangle.
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i need help like immediately
1/4 (8x+4)=2x-4
Answer: the statement is false
Step-by-step explanation:
Headphones were bought for $44. Coupon code got 20% off then a 5% processing fee was after the discount. How much was the processing fee?
The processing fee was = $36.96
what is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
let the price of headphones be= x
44*20/100=8.844-8.8=35.235.2*5/100=1.7635.2+1.76= 36.96Hence,The processing fee was = $36.96
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At a sale, suits were sold for $130 each. If the suits originally cost $200 each, what percentage of its original price was a suit sold for?
Answer:
70%
Explan your answer :
200-130=70 and 70% of 100 = 30% so
Answer: 65
Step-by-step explanation:
0.65
×
100
=
0.65×100=
65
%
65%
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Skill plans
At a candy store, Dean bought 2 kilograms of jelly beans and 3 kilograms of gummy worms
for $38. Meanwhile, Sue bought 3 kilograms of jelly beans and 3 kilograms of gummy worms
for $45. How much does the candy cost?
A kilogram of jelly beans costs $
and a kilogram of gummy worms costs $
The price of one kilogram of jelly bean and gummy worms is $7 and $8 respectively.
Let the price of 1 kilogram of jelly bean cost be x
and the price of 1 kilograms of gummy worms be y
Dean bought 2 kilograms of jelly beans and 3 kilograms of gummy worms
for $38
2x + 3y = 38......equation 1
Sue bought 3 kilograms of jelly beans and 3 kilograms of gummy worms
for $45
3x + 3y = 45........equation 2
Subtracting equation 2 from equation 1
2x + 3y - (3x + 3y) = 38 - 45
2x - 3x + 3y - 3y = -7
-x = -7
x = 7
2(7) + 3y = 38
14 + 3y = 38
3y = 24
y = 8
Therefore, the price of one kilogram of jelly bean and gummy worms is $7 and $8 respectively.
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what is the slope of a line that passes through points (7,-5) and (16,7)
in terms of i.
PLEASE HELP!!
Answer:
[tex]-4i\sqrt{3}[/tex]
Step-by-step explanation:
Answer:
[tex] - 4 \sqrt{3i} [/tex]
Tim, Paco, Maria, and Jenny are standing in line for lunch. Jenny is standing between Paco and Maria, and Paco’s position in line is an odd number. Tim is not standing on either end of the line, and he is in front of Jenny.
Which friend is standing first in line?
Answer:
Paco, Tim, Jenny, Maria
Step-by-step explanation:
it was 5 degrees above zero in the morning. By afternoon the temperature rose 27 degrees. How warm was it?
It was 33 degrees warm in the afternoon
How to determine how warm it was?From the question, we have the following parameters that can be used in our computation:
In the morning = 5 degrees above zero
Afternoon = Rise of 27 degrees
The degree of warmth in the afternoon is then calculated as
Degree of warmth = Temperature In the morning + Rise of the temperature
Substitute the known values in the above equation, so, we have the following representation
Degree of warmth = 5 + 27
Evaluate the sum
Degree of warmth = 33
Hence, the temperature is 33 degrees
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the cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes. what is the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes?
The probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes is 0.25 .
What is probability?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.
A highway construction site's cycle time for trucks transporting concrete is evenly spread over the range of 50 to 70 minutes, thus a = 50 and
b = 70
f(x) = 1/[b - a] = 1/[70 - 50] = 1/20 = 0.05, thus a uniform distribution.
Let P(cycle time is less than 65 minutes if it is known that the cycle time exceeds 55 minutes) be:
P(60 < X < 65) = ₆₀∫⁶⁵ f(x) dx = ₆₀∫⁶⁵ (0.05) dx = 0.05*[65 - 60] = 0.05*5
= 0.25
Thus, the probability that the cycle time exceeds 65 minutes if it is known that the cycle time exceeds 60 minutes is 0.25 .
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an insurance company won't repair a car when the cost of the repair is 25% or more of the car's value. if a repair costs $1400, what is the value of the car (in interval notation)?
The interval of the cost of the car is [5600, ∞).
Here we have to find the cost of the car.
Let x be the cost of the car.
So from the question, we have that the cost of the repair is 25% or more of the car's value.
So we have to find the interval notation of the cost of the car.
x ×25% ≥ 1400
x × 25/100 ≥ 1400
x ≥ 1400× 100/25
x≥ 5600
So we get that the cost of the car is greater than $5600.
Therefore the cost of the car in an interval is [5600, ∞)
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How do I find the measure of the triangles? Help.
Answer:
Step-by-step explanation: I am guessing that it is 180
(3x-19)
what is the value of x
What does 3x-19 equal? You can find x without it being an equation
The solution is, the value of x is 6.33.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
(3x-19) = 0,
here, we have to make the given expression simple, as we have to find the value of x.
so, we get, by isolating the variable & numbers,
adding 19 on both sides we get,
3x = 19
dividing both sides by 3, we get,
or, x = 19/3
or, x = 6.33
Hence, The solution is, the value of x is 6.33.
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Identify all of the roots of f(x) = x² + 2x + 2.
Answer: -1-1i and -1+1i
Step-by-step explanation:
Help! What is the domain of the graph shown below?
A. All real numbers greater than 0.
B. All real numbers greater than -2
C. All real numbers between -5 and 4
D. All real numbers
Answer:
D
Step-by-step explanation:
there are no restrictions on the domain and
- ∞ < x < ∞
That is the domain is all real numbers
In the diagram below, \overline{TU} TU is parallel to \overline{QR} QR . If TUTU is 55 less than TSTS, QS=45QS=45, and QR=36QR=36, find the length of \overline{TS} TS . Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
The length of TS, using similar triangles, is given as follows:
TS = x = 25.
What are similar triangles?Similar triangles are two triangles that share these two features:
Same angle measures.Proportional side lengths.In the context of this problem, the similar triangles are given as follows:
STU and SQR.
The proportional side lengths from these two similar triangles are given as follows:
TS = x and QS = 45.TU = x - 5 and QR = 36.Hence the proportional relationship that relates these lengths on the similar triangles is given as follows:
x/45 = x - 5/36
Applying cross multiplication, the length of TS, equals to x, is obtained as follows:
45(x - 5) = 36x
45x - 225 = 36x
9x = 225
x = 225/9
x = 25.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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The model shows that 3 1/5 divided by 4/5 = 4.
What happens if you divide by 8/5 instead of 4/5
The solution after divide by 8/5 instead of 4/5 will be 2.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Or, A number which is expressed as a quotient is called fraction.
It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The model shows that 3 1/5 divided by 4/5 = 4.
Now,
Substitute 8/5 instead of 4/5, we get;
⇒ 3 1/5 ÷ 8/5
⇒ 16/5 ÷ 8/5
⇒ 16/5 × 5/8
⇒ 2
Thus, The solution after divide by 8/5 instead of 4/5 will be 2.
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Answer:
Step-by-step explanation:
7(x+4)-2[x-3(5+x)]=2/3(x-6)
Hope this helps! Bye, have a nice day!
in a region where we have had big earthquakes (magnitude 7 and above) roughly every 200 years, what is the probability that we will not have a big earthquake in this region in the next two years?
There is a 0.990025 probability that this area won't experience a major earthquake in the next two years.
Define probability.In the field of mathematics called probability theory, random occurrences are studied. The outcome of a random event can take any number of distinct shapes, but it cannot be anticipated before it occurs. The outcome is believed to have been decided by chance.
Given,
In a region where large earthquakes of magnitude 7 or higher have occurred about once every 200 years,
First, the likelihood of an earthquake with a magnitude of 7 or higher is 1/200 = 0.005.
The likelihood of there not being an earthquake is then requested, and it is 1-0.005 = 0.995.
The likelihood that there won't be an earthquake in two years is then
0.995 x 0.995, or.0990025.
The probability that we will not have a big earthquake in this region in the next two years is 0.990025.
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the motel in the preceding example uses approximately600 bars of soap each day, and this tends to be fairly constant. lead time for soap delivery is normally distributed with a mean of six days and a standard deviation of two days. a service level of 90 percent is desired. the re-order point (rop) is:
The re-order point (ROP) for the new batch of the bars of soaps be placed when there is 4800 bars left in the inventory.
Define the term reorder point (ROP)?An exact level where the your stock has to be restocked is characterized as a reorder point (ROP). To put it another way, it advises you when to order so that you won't run out of supply.You'll need to be aware of the following factors in order to figure out the ROP for every item:Lead period: Days needed (in days) for the vendor to complete your orderSafeguard stock: The quantity of excess stock, if any, you maintain on hand to assist prevent stockoutsDaily usage: Average number of sales that particular item typically sees per day.ROP = (Daily usage x Lead period) + Safeguard stock
For the given question;
Lead time = 6 days
Safety stock = 2 days x 600 bars = 1200 bars
ROP = (600 x 6) + 1200 = 4800 bars.
Thus, the re-order point (ROP) for the new batch of the bars of soaps be placed when there is 4800 bars left in the inventory.
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find y when x=17 if y varies directly as x, and y=43 when x=11
The value of y when x = 17 is 66.5
How to determine the value of y?From the question, we understand that:
The variation is a direct variation
The equation of a direct proportion can be represented as
y = kx
Where:
y = independent variablek = constant of proportionalityx = independent variableFrom the question, we have
When x = 11, we have = 43
So, we have
11k = 43
Make k the subject
k = 43/11
Substitute k = 43/11 in y = kx
y = 43/11x
When x = 17, we have
y = 43/11 x 17
This gives
y = 66.5
Hence, the value of y is 66.5
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i need help pls ahhhhh
Answer:
here is the answer have a good day
Answer:
1. 40/5=8
8 x 3p=24p
8(3p+5)=24p+40
2. 48/8=6
64/8=8
8(6q-8)=48q-64
This shows a figure.
What is the measure of angle n?
65\degree65°
70\degree70°
110\degree110°
115\degree115°
To find the value of n we first have to find the value of angle m. because we know the sum of angle m and angle n would be equal to 180 degrees as they both lie on a straight line. to find angle m we have to use the angle sum property of a triangle which says the sum of all the internal angles of a triangle is equal to 180 degrees.
so using the angle sum property,
65+45+m = 180
m= 180-65-45
m=70
now we know m is 70 degrees
for n,
m+n = 180 -(i)
putting m=70 in equation (i)
70 + n = 180
n = 180-70 = 110 degree
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Answer: What??
Step-by-step explanation: