The volume of solid B is about 7π cubic meters, which is approximately 21.99 cubic meters when rounded to the nearest thousandth.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Since solids A and B are similar, they have the same shape, but different sizes.
Let V₁ be the volume of solid A, and V₂ be the volume of solid B. The scale factor k from solid A to solid B is 1/4, which means that the dimensions of solid B are 1/4 of the dimensions of solid A.
We can find the radius and height of solid B by multiplying the radius and height of solid A by 1/4. Therefore, we have:
V₂ = π(r/4)²(h/4) = (π/16)rh²
We are given that V₁ = 112π cubic meters, so we can solve for rh²:
112π = πr²h
rh² = 112
Substituting into the formula for V₂, we get:
V₂ = (π/16)rh² = (π/16)(112) = 7π
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I need help on this question
Answer:
Step-by-step explanation:
I think it’s b
An experiment consists of rolling two fair number cubes. The diagram shows the sample space of all equally likely outcomes. What is the probability of rolling two 3's? Express your answer as a fraction in simplest form.
the probability of rolling two 3's is 1/36.Since we are rolling two number cubes, the sample space contains 6x6 = 36 equally likely outcomes, one for each possible pair of numbers that can be rolled.
what is probability ?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is calculated as the number of ways the event can occur, divided by the total number of possible outcomes.
In the given question,
Since we are rolling two number cubes, the sample space contains 6x6 = 36 equally likely outcomes, one for each possible pair of numbers that can be rolled.
To find the probability of rolling two 3's, we need to count the number of outcomes that result in two 3's, and divide by the total number of possible outcomes.
From the diagram, we can see that there is only one outcome that results in two 3's, namely the outcome where the first cube shows a 3 and the second cube shows a 3. Therefore, the number of favorable outcomes is 1.
The probability of rolling two 3's is therefore:
P(rolling two 3's) = favorable outcomes / total outcomes = 1/36
So the probability of rolling two 3's is 1/36.
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(ASAP!) In the diagram the smaller triangle is an image of the larger triangle. a) Name the angle in the image that corresponds to in the preimage. b) List all pairs of corresponding sides.
1. ∠B is the primage of ∠B'. They are similar triangles.
2. AC ≈AC'
CB ≈ CB'
AB ≈ AB'
what is meant by the preimage when discussing angles?When discussing angles, the preimage refers to the original angle before any transformation has occurred.
In geometry, a transformation refers to the process of moving or changing the position, shape, or size of an object. For example, if an angle is rotated or reflected, the resulting image of the angle would be the transformed angle.
The preimage is the angle before the transformation occurred. It is used to determine the relationship between the original angle and the transformed angle, such as whether they are congruent, similar, or related by another geometric property.
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What is the value of x when -3x + 7x = -12?
A -6/5
B -3
C 6/5
D 4/7
E 3
I NEED AN ANSWER ASAP!
An official NHL hockey puck is shaped like a cylinder with a diameter of 3 inches and a volume of 7.1 cubic inches. What is the height of a hockey puck?
Answer: the height of the hockey puck is approximately 0.835 inches.
Step-by-step explanation: The formula for determining the volume of a cylinder is as follows:
The formula for the volume (V) of a cylinder can be expressed mathematically as V = πr2h, where r represents the radius of the cylinder's base and h represents the height of the cylinder. This formula is derived from the concept that the volume of a cylinder can be calculated by multiplying the area of its base (which is represented by the term πr2) by its height (h).
The present study utilizes the conventional nomenclature in which V denotes the volume, r represents the radius, and h stands for the height.
As the diameter of the hockey puck is measured to be 3 inches, it follows that the radius is equivalently calculated as 1.5 inches, or precisely half of the diameter.
It is established that the hockey puck has a volume of 7.1 cubic inches; accordingly, by substituting these known values into the relevant formula and performing the appropriate calculations, the measurement of h may be ascertained.
The expression 7.1 = π(1.5)^2h can be reformulated in a more academic manner. It can be said that the equation represents the mathematical relationship between the volume of a cylinder and its dimensions, wherein the value of 7.1 denotes the volume of the cylinder, whereas π, 1.5, and h refer to the mathematical constants of pi, radius, and height, respectively. Thus, the formula can be expressed as V = πr^2h, where V represents the volume of the cylinder, r denotes the radius, and h denotes the height.
The process of reducing something to its simplest form. Rewritten: The act of simplification involves distilling a concept or idea to its most basic, essential components. This process aims to facilitate a clear and concise understanding of the subject matter, allowing for greater comprehension and ease of communication.
The numerical expression 7.1 = 2.25πh can be written in a more formal and academic manner. Specifically, the equation can be rephrased as an algebraic relationship between the variables involved. More concisely, the equation describes the result of a multiplication between the constant factor 2.25π and the variable h, which according to the equation equals 7.1. As such, it can be represented by the following expression: 2.25πh = 7.1
Dividing each side by 2.25π is a logical mathematical operation utilized to simplify an equation or expression.
The aforementioned equation may be expressed in an academic tone as follows: The value of h is equivalent to the quotient obtained from dividing 7.1 by 2.25 times the mathematical constant π.
The employment of a calculator to compute the aforementioned expression:
The observed value of h is approximately equal to 0.835 inches.
Billy has a credit card with a current balance of $3,500 and a 16% APR. With his current monthly payment, he will be able to pay off this debt in 15 months. But Billy just learned that he is getting a raise at work. If he puts all of the extra income from his raise into his monthly credit card payment, how much additional monthly income would he require from his raise to pay off the credit card in 12 months? a. $58.57 b. $171.37 c. $258.99 d. $317.56
Answer:
a. $58.57
Step-by-step explanation:
Billy is in a pickle. He has a credit card debt of $3500 with a 16% annual interest rate, and he wants to pay it off in a year. He also wants to ask his boss for a raise, but he doesn't know how much to ask for. Luckily, he has a friend who is good at math and can help him out.
The friend tells Billy that we need to use the formula for the monthly payment of a credit card debt, which is:
P = (r / 12) * B / (1 - (1 + r / 12)^(-n))
where P is the monthly payment, r is the annual interest rate, B is the current balance, and n is the number of months to pay off the debt.
Using this formula, the friend calculates how much Billy is currently paying and how much he would need to pay to clear his debt in 12 months. The friend also finds the difference between these two payments, which is the amount of extra income Billy would need from his raise.
The friend shows Billy the calculations and says:
"Here you go, Billy. You are currently paying $280.42 per month to pay off your debt in 15 months. If you want to pay it off in 12 months, you would need to pay $331.79 per month. That means you would need an additional monthly income of $51.37 from your raise. The closest answer choice to this amount is a. $58.57, so this is the best option."
Billy thanks his friend and says:
"Wow, you are amazing! Thank you so much for helping me out. I'm going to ask my boss for a raise right now. Wish me luck!"
The friend wishes Billy good luck and hopes that he will get his raise and pay off his debt soon.
Plot and connect the points A (6, -7), B (1, -7), C (1, -4), D (3, -2), E (7. -2), F (7,-4), and find the length of AB.
OA. 6 units
O B.
7 units
O C.
5 units
D. 8 units
Using distance formula, the distance between AB is 5 units and the graph of the coordinates from A to F are attached below
What is the length of ABTo find the length of AB, we have to use distance formula which is given as
AB = √(x₂ - x₁)² + (y₂ - y₁)²
substituting the values into the equation;
AB = √(1 - 6)² + (-7 - (-7))²
AB = 5
The length of line AB is 5 units
To plot the points from A to F, we have to use a graphing calculator, input the points and draw all lines
Kindly find the attached graph of all the coordinates from A to F below
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units Answer:
5
Step-by-step explanation:
engineers designing the next generation of space shuttles plan to include two fuel pumps - one active, the other in reserve. if the primary pump malfunctions, the second is automatically brought on line. suppose a typical mission is expected to require that fuel be pumped for at most 50 hours. according to the manufacturer?s specifications, pumps are expected to fail once every 100 hours. what are the chances that such a fuel pump system would not remain functioning for the full 50 hours?
The probability that this particular fuel pump system when put into the required condition would not remain functional for the full 50 hours is 0.0199.
Therefore, the probability of a fuel pump failing in a mission can be evaluated using the formula designed for probability of failure in a system with two pumps in series connection
P(failure) = P(pump 1 fails) + P(pump 2 fails) - P(both pumps fail)
Here
P(pump 1 fails) = P(pump 2 fails) = 0.01
P(both pumps fail) = (0.01)² = 0.0001.
Now,
P(failure) = 0.01 + 0.01 - 0.0001 = 0.0199
The probability that this particular fuel pump system when put into the required condition would not remain functional for the full 50 hours is 0.0199.
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Given that f(x)=x-9,g(x) = 3x^2- 2x + 5, and h(x)=-6x, find each function.
(f+h)(x)=
216,36,6,... Find the 8th term. Find the 8th term.
Answer:
t8 term is
[tex] \frac{ 1}{1296} [/tex]
Find the domain and range of the exponential function h(x) = 125x. Explain your findings. As x decreases, does h increase or decrease? Explain. As x increases, does h increase or decrease? Explain. need anwsred ASAP
The domain is all real numbers, range is all positive real numbers. As x decreases, h(x) will decrease. As x increases, h(x) will increase.
The domain of the exponential function h(x) = 125x is all real numbers, as x can take on any value.
The range of the function is all positive real numbers, as the base (125) raised to any power (x) will always be positive.
As x decreases, h(x) will decrease. This is because when the base of an exponential function is greater than 1, as is the case here with 125, the function increases as the exponent increases, and decreases as the exponent decreases. So, as x becomes more negative, h(x) becomes smaller.
As x increases, h(x) will increase. This is because, as mentioned above, when the base of an exponential function is greater than 1, the function increases as the exponent increases. So, as x becomes more positive, h(x) becomes larger.
Overall, the function h(x) = 125x is an increasing function with a domain of all real numbers and a range of all positive real numbers.
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85 POINTS ASAP 85 POINTS ASAP Polygon ABCD with vertices at A(1, −1), B(3, −1), C(3, −2), and D(1, −2) is dilated to create polygon A′B′C′D′ with vertices at A′(2, −2), B′(6, −2), C′(6, −4), and D′(2, −4). Determine the scale factor used to create the image.
one fourth
one half
2
4
The scale factor used to create the image include the following: C. 2.
What is a scale factor?In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original figure (pre-image).
Mathematically, the formula for calculating the scale factor of any geometric object or figure is given by:
Scale factor = side length of image/side length of pre-image
By substituting the given side lengths or dimensions into the formula for scale factor, we have the following;
Scale factor = 2/1
Scale factor = 2.
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graph the solution set of the inequality -6 1/2y+9>-17
The graph of the solution set can be seen in the image at the end.
How to find the solution set for the inequality?Here we have the inequality:
-(6 + 1/2)y + 9 > -17
First, we need to isolate the variable y, then we will get:
9 + 17 > (6 + 1/2)y
26 > 6.5y
26/6.5 > y
4 > y
The graph of this will be an open circle at y = 4, and an arrow that goes to the left, the graph can be seen in the image at the end.
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cupcake delight shop made 4 1/2 as much revenue on doughnuts as muffins. if total sales were 44,000 what dollar amount of each was sold?
The revenue from muffins was $8,000. To find the revenue from doughnuts: 4.5x = 4.5 * 8,000 = $36,000 Therefore, the cupcake delight shop sold $8,000 worth of muffins and $36,000 worth of doughnuts.
Let's use the given terms and set up a system of equations to solve this problem:
Let x be the revenue from muffins, and y be the revenue from doughnuts. We know the following:
1. y = 4.5x (Cupcake Delight Shop made 4 1/2 times as much revenue on doughnuts as muffins)
2. x + y = 44,000 (Total sales were $44,000)
Now we'll solve the system of equations step-by-step:
Step 1: Replace y with 4.5x in the second equation (using equation 1):
x + 4.5x = 44,000
Step 2: Combine the x terms:
5.5x = 44,000
Step 3: Divide both sides by 5.5 to solve for x:
x = 8,000
Step 4: Plug x back into equation 1 to find y:
y = 4.5 * 8,000
y = 36,000
So, Cupcake Delight Shop sold $8,000 worth of muffins and $36,000 worth of doughnuts.
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The dollar amount of muffins sold is $8,000, and the dollar amount of doughnuts sold is $36,000.
To solve this problem, let's assign variables to the revenue for doughnuts and muffins:
Let D = revenue from doughnuts
Let M = revenue from muffins
We are given that the shop made 4 1/2 times as much revenue on doughnuts as muffins:
D = 4.5M
We are also given that the total sales were $44,000:
D + M = 44,000
Now, we can solve for the dollar amount of each item sold:
Replace D with 4.5M in the second equation:
4.5M + M = 44,000
Combine like terms:
5.5M = 44,000
Divide by 5.5 to isolate M:
M = 44,000 / 5.5
M = 8,000
Plug the value of M back into the first equation to find the value of D:
D = 4.5M
D = 4.5 × 8,000
D = 36,000.
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The population of wild tigers in Nepal can be modeled by the equation LaTeX: p=130\left(2\right)^x
p
=
130
(
2
)
x
, where x is the number of years since 2009.
Part A
Assuming the population growth rate continues, an equation that represents the number of years from 2009 it will take for the population of wild tigers in Nepal to reach 1,000 can be expressed as LaTeX: x=\log_ba
x
=
log
a
b
, where a and b are >0. What are the values of a and b?
Part B
Approximately how many years from 2009 will it take for the population of wild tigers in Nepal to reach 1,000? Round your answer to the nearest whole number
Part A
According to the equation, the values of a is a = 2009 + f(a) and b is b = 800 + f(b).
Part B
Approximately it takes 8 years from 2009 for the population of wild tigers in Nepal to reach 800.
To find these values, we need to set the equation for the population of wild tigers equal to 800 and solve for x. The equation becomes 800 = 121(2)ˣ.
Taking the logarithm of both sides, we get
=> log(800) = log(121) + x log(2).
Solving for x, we get
=> x = (log(800) - log(121))/log(2).
Moving on to the second part of the problem, we are asked to determine approximately how many years from 2009 it will take for the population of wild tigers in Nepal to reach 800. Using the equation we derived in Part A, we can plug in values of a and use trial and error to find the answer. However, this can be time-consuming.
Instead, we can use a calculator to get an approximate answer. Plugging in the values for log(800) and log(121) into the equation we derived in Part A, we get x = 7.75.
Therefore, it will take approximately 8 years from 2009 for the population of wild tigers in Nepal to reach 800.
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Ashley and Nicole are at softball practice. Ashley hits a softball 65 meters. Nicole hits a soft ball 6,700 centimeters. who hit the softball farther, Ashley or Nicole
Answer: Ashley hit the softball farther.
Step-by-step explanation: Ashley hit the softball farther, since her distance of 65 meters is greater than Nicole's distance of 6,700 centimeters.To compare these distances, we need to convert Nicole's distance from centimeters to meters, since Ashley's distance is given in meters.To do this, we can divide Nicole's distance by 100, since there are 100 centimeters in a meter:6700 cm / 100 cm/m = 67 mTherefore, Ashley hit the softball 65 meters, which is less than the 67 meters that Nicole hit it. This means that Ashley hit the softball farther.
A box measures 48 inches long, 22 1/2 inches wide, and 32 inches high. What is the volume of the box
The volume of the box should be 34,560 cubic inches.
v=l*w*h
v=48*22.5*32
(22 1/2 = 22.5)
v=34,560
If the area was equal to 8w solve to find the values of w.
A=2w^2 - 16w
Answer:
hence the value of w is 12
Step-by-step explanation:
[tex]area = 2 {w}^{2} - 16w \\ by \: the \: question \: if \: area \: is \: equal \: to \: 8w \\ 8w = 2w {}^{2} - 16w \\ 8w + 16w = 2 {w}^{2} \\ 24w = 2 w {}^{2} \\ w = 12[/tex]
A rectangular box has a volume of 3,840 cubic inches. The length of the box is 20 inches and the height of the box is 16 inches. Determine the width of the box. Question 4 options: 11 inches 12 inches 13 inches 14 inches
The width of the rectangular box is 12 inches.
How to determine the width of the rectangular box?Remember that the volume of a box of length L, width W, and height H is:
V = H*W*L
Here the volume is 3,840 cubic inches. The length of the box is 20 inches and the height of the box is 16 inches. Replacing that in the formula we will get:
3840 = 20*16*W
Solving that for W we will get:
3840/(20*16) = W
12 = W
The width is 12 inches.
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A rectangle has the following dimension:
Length (x+1) cm
Width x cm.
Find the perimeter of the retangle.
A.(4x+2) cm^2
B.(2x+1) cm
C.(2x+1) cm^2
D.(4x+2) cm
Answer:
The process is below and the answer is D.
Step-by-step explanation:
[tex]perimeter \: = 2(l + b) \\ = 2((x + 1)cm + xcm) \\ = 2(x + 1 + x) \\ = 2(2x + 1)[/tex]
[tex](4x + 2)cm[/tex]
I hope it helped you
please Mark me the brainliest
Convert 2.340 x 10-4 to decimal format.A) 23,400 B) 2,340 C) 0.000234 D) 0.0002340 E) 0.002340
After converting 2.340 x 10⁴ to decimal format we will be getting 0.000234. So, the correct answer choice is options (C) which is 0.000234.
In order to convert the given epression i.e. 2.340 x 10⁴ to decimal format, we are required to move the decimal point four places to the left since the exponent is negative.
In order to find the correct decimal format, starting with 2.340, we move the decimal point four places to the left, then the value we will be getting is equal to 0.000234
Therefore, from the above calculation we can draw the inference that the correct answer is option C) i.e 0.000234.
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If x=4 units, y=6 units , and h= 5 units, find the area of the rhombus shown above using decomposition. Please help
the area of the rhombus is approximately 74.60 square units.
How to solve the question?
To find the area of a rhombus using decomposition, we first need to draw its diagonal lines. Let's label the points where the diagonals intersect as points A and B.
Now we can decompose the rhombus into two congruent triangles, ABC and ABD, where AB is the diagonal and AD and BD are half of the diagonals.
We can find the length of AD and BD using the Pythagorean theorem. Since x=4 units and y=6 units, we have:
AD²= (x/2)² + h²
AD² = (4/2)²+ 5²
AD²= 4² + 5²
AD² = 41
AD = sqrt(41)
Similarly, we can find the length of BD:
BD²= (y/2)² + h²
BD²= (6/2)² + 5²
BD²= 3²+ 5²
BD²= 34
BD = √(34)
Now we can find the area of each triangle:
Area of ABC = (AB * BD) / 2
Area of ABC = (2 * √(41) * √(34)) / 2
Area of ABC = √(1394)
Since the rhombus is made up of two congruent triangles, its total area is twice the area of one triangle:
Area of rhombus = 2 * Area of ABC
Area of rhombus = 2 * √(1394)
Area of rhombus ≈ 74.60 square units
Therefore, the area of the rhombus is approximately 74.60 square units.
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uppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. when carrying gallons of fuel, the airplane weighs pounds. when carrying gallons of fuel, it weighs pounds. how much does the airplane weigh if it is carrying gallons of fuel?
The weight of the plane if it is carrying gallons of fuel is 2336 pounds, under the condition of when carrying 10 gallons, and 45 gallons he airplane weighs 2056 and 2252 pounds.
We can utilize the two given points to create two linear equations
y = mx + b
2056 = 10m + b
2252 = 45m + b
We can find m and b by subtracting the first equation from the second equation:
(45m + b) - (10m + b) = 2252 - 2056
35m = 196
m = 5.6
For finding b by substituting m into one of the original equations:
2056 = 10(5.6) + b
b = 2000
The equation is
y = 5.6x + 2000
To evaluate how much the airplane weighs when carrying 60 gallons of fuel, now lets substitute x into the equation
y = 5.6(60) + 2000
y = 336 + 2000
y = 2336
The weight of the plane if it is carrying gallons of fuel is 2336 pounds, under the condition of when carrying 10 gallons, and 45 gallons he airplane weighs 2056 and 2252 pounds.
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The complete question is
Suppose that the weight (in pounds) of an airplane is a linear... Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 10 gallons of fuel, the airplane weighs 2056 pounds. When carrying 45 gallons of fuel, it weighs 2252 pounds. How much does the airplane weigh if it is carrying 60 gallons of fuel?
this is due now pls explain how to do this
Answer:
C. Vertical angles
Step-by-step explanation:
Given angles 5 and 8 where line c crosses line a, you want to know what type they are.
Crossing linesWhere two lines cross, four angles are formed. They all share the vertex point where the lines intersect. If they share a side (and no interior space), they are adjacent angles that form a linear pair. As such, they are supplementary.
In the given figure the supplementary angle pairs where line c crosses line a are ...
(5, 6), (6, 8), (7, 8), (5, 7)
If the angles do not share a side, but are formed from opposite rays, they are "vertical angles" and are congruent.
The vertical angle pairs there are ...
(5, 8), (6, 7)
Angles 5 and 8 are vertical angles, choice C.
__
Additional comment
Angle pairs (1, 8) and (2, 7) are "alternate exterior angles." Angle pairs (3, 6) and (4, 5) are "alternate interior angles."
Assuming lines b and c are parallel, considering also angles where line b crosses line a, there are additional supplementary pairs of angles:
(1, 2), (2, 4), (3, 4), (1, 3), (1, 6), (1, 7), (2, 5), (2, 8), (3, 5), (3, 8), (4, 6), (4, 7)
When parallel lines are crossed by a transversal, all of the acute angles are congruent, all of the obtuse angles are congruent, and the acute angles are supplementary to the obtuse angles. The angles are referred to by different names (and different theorems), depending on where they are in relation to the transversal and the parallel lines.
The problem here is mostly concerned with vocabulary. The "how to do this" is "learn the vocabulary."
<95141404393>
|4x-4(x+1)|=4
put all answers for x on number line
In the bottom, To see the number line of |4x-4(x+1)|=4.
Absolute Value:The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.
The expression is:
|4x-4(x+1)|=4
First simplify in the absolute value
Distribute
|4x−4x-4|=4
|-4|=4
Taking the absolute value
4 =4
This is always true
X is all real numbers
Pick any value for x and it will be a true statement
Put the value of x=0
|4*0−4(*0+1)|=4
|-4|=4
Let taking a value of x = 5
|4*5−4(5+1)|=4
|20−24|=4
|−4|=4
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There are 3 red pens and 12 black pens in a package, which ratio is equivalent to 3/12
Therefore , the solution of the given problem of ratio comes out to be this indicates that there are 4 black pens in the package for every red pen.
What is a ratio?A group comprising values both variable "a" and "" that seem to be equal is found using the straightforward formula "a / b," whenever "b" might be a greater number than zero. A ratio is created by combining two ratios. The ratio , fraction could have been 1:1 if there were just one guy and three women. There are 1/4 men and 3/4 women in the group.
Here,
By dividing the numerator and denominator by their greatest common divisor (GCD), the ratio 3/12 can be made simpler.
Due to the fact that both 3 and 12 can be divided by 3, their GCD equals 3.
The result of dividing the numerator and denominator by 3 is:
=> 3 ÷3 = 1.
=> 12 ÷ 3 = 4
Thus, 1/4 is the simple ratio that corresponds to 3/12.
Let's now use a simplified equivalent ratio to represent the ratio of red to black pens in the package:
Black pens 3: 12 Red pens:
=> 3 ÷ 3 = 1
=> 12 ÷ 3 = 4
Consequently, the rounded equivalent ratio of red to black pens is 1 to 4.
This indicates that there are 4 black pens in the package for every red pen.
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write a function that models the total amount of money Julia has after x weeks use x
The function that models the total amount of money Julia has after x weeks is f(x) = 27x + 254
How to solve an equation?An equation is an expression that uses mathematical operations to show how numbers and variables are related to each other.
Let f(x) represent the total amount of money Julia has after x weeks.
Julia has $254 and saves $27 each week, hence:
f(x) = 27x + 254
The function is f(x) = 27x + 254
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If f(1)=4 and f(n)=-3f(n-1) , then find the value of f(6).
the value of f(6) is -972.To understand why f(6) is equal to -972, we can think of the recursive formula as a process that generates a sequence of numbers. Starting with f(1) = 4, we can apply the formula repeatedly to generate the sequence:
4, -12, 36, -108, 324, -972, ...
How to solve the question?
We can use the recursive formula given to find the value of f(6). Let's start by calculating f(2):
f(2) = -3f(1) = -3(4) = -12
Next, we can calculate f(3) using the same formula:
f(3) = -3f(2) = -3(-12) = 36
We can continue this process for f(4) and f(5):
f(4) = -3f(3) = -3(36) = -108
f(5) = -3f(4) = -3(-108) = 324
Finally, we can use the formula to find f(6):
f(6) = -3f(5) = -3(324) = -972
Therefore, the value of f(6) is -972.
To understand why f(6) is equal to -972, we can think of the recursive formula as a process that generates a sequence of numbers. Starting with f(1) = 4, we can apply the formula repeatedly to generate the sequence:
4, -12, 36, -108, 324, -972, ...
Each term in the sequence is obtained by multiplying the previous term by -3. We can see that the sequence alternates between positive and negative values, with the magnitude of each term growing rapidly. By the time we reach f(6), the magnitude has grown to 972, and the negative sign indicates that the term is negative. Thus, f(6) is equal to -972.
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Find an equation for the perpendicular bisector of the line segment whose endpoints
are(-1, , -8) and (5, 4).
An equation in slope-intercept form for the perpendicular bisector of the line segment with endpoints (-1, -8) and K (5, 4) is y = 2x - 6.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 + 8)/(5 + 1)
Slope (m) = 12/6
Slope (m) = 2.
At data point (-1, -8) and a slope of 2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-8) = 2(x - (-1))
y + 8 = 2x + 2
y = 2x - 6.
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What is the value of the following expression?
2 + [(15 + 3) × 2]
Step-by-step explanation:
The value of the expression can be calculated using the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
The expression is:
2 + [(15 + 3) × 2]
According to PEMDAS, we should first evaluate the expression within the parentheses:
15 + 3 = 18
So, the expression becomes:
2 + [18 × 2]
Next, we perform the multiplication:
18 × 2 = 36
Now, we substitute the result back into the original expression:
2 + 36
Finally, we perform the addition:
2 + 36 = 38
So, the value of the given expression is 38.