The basic subtraction of rational expression simplified is (7)/(12d).
To subtract these rational expressions, we need to find a common denominator. The least common denominator (LCD) of 4d and 6d is 12d. We can then rewrite the expressions with the LCD as the denominator:
(3)/(4d) = (3 * 3)/(4d * 3) = (9)/(12d)
(1)/(6d) = (1 * 2)/(6d * 2) = (2)/(12d)
Now we can subtract the numerators and keep the same denominator:
(9)/(12d) - (2)/(12d) = (9 - 2)/(12d) = (7)/(12d)
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 1:
(7)/(12d) = (7/1)/(12d/1) = (7)/(12d)
So the final answer is (7)/(12d).
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At the beginning of 2019, there were an estimated 295,382 women living with cervical cancer in the United States.
During 2019, there were an additional 346 women newly diagnosed with cervical cancer. There were an estimated 166,238,619 women living in the United States in 2019. What was the incidence of cervical cancer among women in the United States in 2019?
Answer: To calculate the incidence of cervical cancer among women in the United States in 2019, we need to divide the number of new cases (346) by the total population at risk (i.e., the number of women without cervical cancer) and then multiply by 100,000 to express the result per 100,000 women.
Number of women without cervical cancer = Total number of women - Number of women with cervical cancer
Number of women without cervical cancer = 166,238,619 - 295,382
Number of women without cervical cancer = 165,943,237
Incidence of Cervical Cancer = (New cases / Number of women without cervical cancer) x 100,000
Incidence of Cervical Cancer = (346 / 165,943,237) x 100,000
Incidence of Cervical Cancer = 0.21 per 100,000 women
Therefore, the incidence of cervical cancer among women in the United States in 2019 was 0.21 per 100,000 women.
Step-by-step explanation:
Consider the line ( y=7 x-7) Find the equation of the line that is parallel to this line and passes through the point (-6,6) . Find the equation of the line that is perpendicular to this line
The equation of the line that is parallel to the line y = 7x - 7 and passes through the point (-6,6) is y = 7x + 48. The equation of the line perpendicular to the resulting line is y = (-1/7)x + 36/7.
To find the equation of a line that is parallel to another line and passes through a given point, we can use the slope-intercept form of a line (y = mx + b), where m is the slope and b is the y-intercept.
Since parallel lines have the same slope, the slope of the new line will also be 7.
To find the y-intercept, we can plug in the given point (-6, 6) into the equation and solve for b:
6 = 7(-6) + b
b = 6 + 42
b = 48
So the equation of the parallel line is y = 7x + 48.
To find the equation of a line that is perpendicular to another line, we can use the fact that the slope of a perpendicular line is the negative reciprocal of the original slope. So the slope of the perpendicular line will be -1/7.
Again, we can plug in the given point (-6, 6) into the equation and solve for b:
6 = (-1/7)(-6) + b
b = 6 - 6/7
b = 36/7
So the equation of the perpendicular line is y = (-1/7)x + 36/7.
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Find the minimum and maximum values of z=7x+3y , if possible, for the following set of constraints.
4x + 6y ≥ 24
x + 6y ≥ 12
x ≥ 0, y ≥ 0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The minimum value is (Round to the nearest tenth as needed.) B. There is no minimum value.
The minimum value is 24
To find the minimum value of z=7x+3y, we must use the given constraints to determine the values of x and y.
First, solve 4x + 6y ≥ 24. Rearrange the equation to solve for x: x ≥ (24 - 6y) / 4.
Next, solve x + 6y ≥ 12. Rearrange the equation to solve for y: y ≥ (12 - x) / 6.
Using the two equations, determine the possible values of x and y:
If y = 0, then x = 6
If x = 0, then y = 2
Substitute the possible values of x and y into the equation z = 7x + 3y and find the minimum value:
z = 7(6) + 3(0) = 42
z = 7(0) + 3(2) = 24
Therefore, the minimum value of z is 24.
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6.
Erin and Christa were working on cubing
binomials for math homework. Erin believed they
could save time with a shortcut. She wrote down
the rule below for Christa to follow.
(a + b)³ = a³ + b³
Does Erin's shortcut always work? Justify your
result algebraically.
PLEASE SHOW WORK
If Erin and Christa were working on cubing binomials for math homework. Erin's shortcut does not always work and should not be used.
Does Erin's shortcut always work?Erin's shortcut is not correct. To see why, let's expand (a+b)³ using the binomial theorem: :
(a+b)³ = (a+b)(a+b)(a+b)
= (a+b)(a²+2ab+b²)
= a³ + 2a²b + ab² + a²b + 2ab² + b³
= a³ + 3a²b + 3ab² + b³
So the correct expansion of (a+b)³ has four terms, not two as Erin's shortcut suggests. Therefore, Erin's shortcut does not always work and should not be used.
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What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
The area of the triangle is approximately 6.696 square feet.
What is Area of Triangle?
The area of a triangle is the amount of space enclosed by the three sides of the triangle
To find the area of a triangle with two sides and the included angle, we can use the following formula:
Area = (1/2) x a x b x sin(C)
where "a" and "b" are the lengths of the two sides and "C" is the angle between them.
Substituting the given values, we get:
Area = (1/2) x 3.2 ft x 4.7 ft x sin(62 degrees)
Using a calculator, we can evaluate sin(62 degrees) to be approximately 0.88.
So, Area = (1/2) x 3.2 ft x 4.7 ft x 0.88
= 6.696 ft²
Therefore, the area of the triangle is approximately 6.696 square feet.
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Answer:
The answer is 6.64 ft^2
Step-by-step explanation:
Suppose the total length of the guitar is given by the expression 8 147. Which radical expression represents the length of the body if the neck measures 8 48 ?
The length of the body of the guitar is represented by the radical expression 24√3.
We can start by simplifying 8√147.
8√147 = 8√(49 × 3) (since 49 is a perfect square)
= 8 × 7√3
= 56√3
Next, we need to find the length of the body of the guitar, given that the neck measures 8√48. We know that the total length of the guitar is 56√3, so we can set up an equation:
total length = length of neck + length of body
56√3 = 8√48 + length of body
To solve for the length of the body, we can start by simplifying 8√48:
8√48 = 8√(16 × 3) (since 16 is a perfect square)
= 8 × 4√3
= 32√3
Substituting this back into the equation:
56√3 = 32√3 + length of body
Simplifying:
length of the body = 24√3
Therefore, the answer is A) 24√3.
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The question is -
Suppose the total length of the guitar is given by the expression 8√147. Which radical expression represents the length of the body if the neck measures 8√48? A) 24√3 B) 12√3 C) 8√3 D) 9√9
To get from Boone to Charlotte, you would have to drive about 156.6 km on the shortest route. To get from Boone to Anchorage, AK, you would have to drive 4,212.7 miles. How many orders of magnitude larger is the distance from Boone to Anchorage than Boone to Charlotte? (1 mi = 1.61 km).
Answer: 1.64. To find the difference in orders of magnitude between the two distances, we first need to convert both distances to the same unit of measurement. We'll convert both distances to kilometers.
The distance from Boone to Charlotte is already in kilometers, so we don't need to do any conversion for that distance.
The distance from Boone to Anchorage is in miles, so we'll need to convert that distance to kilometers. To do this, we'll multiply the number of miles by the conversion factor 1.61 km/mi:
4,212.7 mi × 1.61 km/mi = 6,782.45 km
Now that both distances are in kilometers, we can compare them to find the difference in orders of magnitude. An order of magnitude is a factor of 10, so we'll divide the larger distance by the smaller distance and then take the base 10 logarithm of the result:
log10(6,782.45 km / 156.6 km) = log10(43.3) ≈ 1.64
So the distance from Boone to Anchorage is about 1.64 orders of magnitude larger than the distance from Boone to Charlotte.
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Please do the follo When the fraction rewrite it as a mixe integer. 0.6-:2(2)/(11)
The mixed integer would be 2 3/4.
A mixed integer is a number that includes both a whole number and a fraction. For example, 2 1/2 is a mixed integer because it includes the whole number 2 and the fraction 1/2.
To rewrite a fraction as a mixed integer, you need to divide the numerator (the top number) by the denominator (the bottom number) and find the quotient and remainder. The quotient will be the whole number part of the mixed integer and the remainder will be the numerator of the fraction part. The denominator will stay the same.
For example, if you have the fraction 11/4, you can divide 11 by 4 to get a quotient of 2 and a remainder of 3. So the mixed integer would be 2 3/4.
Here are the steps to rewrite a fraction as a mixed integer:
1. Divide the numerator by the denominator.
2. Write the quotient as the whole number part of the mixed integer.
3. Write the remainder as the numerator of the fraction part of the mixed integer.
4. Keep the denominator the same.
5. Simplify the fraction if necessary.
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A, B & C form the vertices of a triangle. ∠ CAB = 90°, ∠ ABC = 49° and AB = 8. 9. Calculate the length of AC rounded to 3 SF
Answer:
/AC/=10.2
Mark as brainliest
A boat traveled downstream a distance of
38
mi and then came right back. If the speed of the current was
6
mph and the total trip took
4
hours and 45 minutes, find
the average speed of the boat relati
The average speed of the boat relative to the water is approximately 17.08 mph.
The average speed of the boat relative to the water can be found by using the formula for distance, speed, and time:
distance = speed × time
We can use this formula to set up two equations, one for the downstream trip and one for the upstream trip:
38 = (s + 6) × t₁
38 = (s - 6) × t₂
We can then use the given information about the total time of the trip to find the values of t₁ and t₂:
4.75 = t₁ + t₂
We can rearrange the first two equations to solve for t₁ and t₂ in terms of s:
t1 = 38/(s + 6)
t2 = 38/(s - 6)
Substituting these values into the third equation and simplifying gives us:
4.75 = 38/(s + 6) + 38/(s - 6)
4.75s² - 57s - 114 = 0
Using the quadratic formula, we can solve for s:
s = (57 ± √(57₂ - 4(4.75)(-114)))/(2(4.75))
s ≈ 17.08 or s ≈ -3.01
Since the speed of the boat cannot be negative, t
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75. Linear Speed at the Equator. The earth has a 4000-mi radius and rotates one revolution every 24 hr. What is the linear speed of a point on the equator, in miles per hour? 76. Linear Speed of the Earth. The earth is about 93,000,000 mi from the sun and traverses its orbit, which is nearly circular, every 365.25 days. What is the linear velocity of the earth in its orbit, in miles per hour?
75. To find the linear speed of a point on the equator, we need to use the formula for the circumference of a circle: C = 2πr. The radius of the earth is 4000 mi, so the circumference of the earth at the equator is C = 2π(4000) = 8000π mi. The earth rotates one revolution every 24 hours, so the linear speed of a point on the equator is 8000π/24 = 333.33π mi/hr ≈ 1047.2 mi/hr.
76. To find the linear speed of the earth in its orbit, we need to use the same formula for the circumference of a circle, but this time the radius is the distance from the earth to the sun, which is 93,000,000 mi. The circumference of the earth's orbit is C = 2π(93,000,000) = 186,000,000π mi. The earth traverses its orbit every 365.25 days, or 8766 hours. So the linear speed of the earth in its orbit is 186,000,000π/8766 = 21,174.6π mi/hr ≈ 66,555.8 mi/hr.
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i ijijiijiiiiiiiiiiiiiiiiiiiiiii
Answer: 1.09 is closer to 1
(a) (9 points) Find the minima and maxima of the following functions at a given interval:y=sin(x)in the interval[2π,4π]. (b) (4 points) Furthermore, determine thexvalues at which maxima and minima occurs. Hints: Please refer to the solveset (equation, variable, Interval (numn1, num2)) function to obtain the value within the given interval. However, solveset() does not return the values as an array. Therefore, it may require further processing. Additionally,πis accessed in SymPy as "sp.pi"
maxima_value = sp.sin(maxima)
minima_value = sp.sin(minima)
For part (a), to find the minima and maxima of the function y=sin(x) in the interval [2π, 4π], you can use the SymPy solves
et() function, which takes an equation, a variable and an interval (numn1, num2) as inputs. To do this, you can use the following code:
minima, maxima = sp.solveset(sp.Eq(sp.sin(x), 0), x, (sp.pi*2, sp.pi*4))
For part (b), to determine the x-values at which the maxima and minima occurs, you can use the minima and maxima values from the previous solveset() function and evaluate the sin(x) at those points. For example:
maxima_value = sp.sin(maxima)
minima_value = sp.sin(minima)
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in ABC m
jjj k
kkkkkkk
kkk
Hey, guys-is this a function? Can you also please explain why with your answer? Thank you for your help, been a long day.
Yes, the graph represents a function.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given ordered pairs from the given graph are (-7, 3), (-3, -3), (0,1), (2, 4), (3, -1), (5, -6)
The given graph represents a relation.
Since each value of x has unique y value.
So the given graph represents a function.
Hence, yes the graph represents a function.
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what is the quotient to 5984 divided by 32
Answer:
The quotient of 5984 divided by 32 is 187.5
Step-by-step explanation:
Answer:
The quotient of 5984 divided by 32 is 187.
What is the slope of the line represented by the equation: y = 7x
Answer: 7
Step-by-step explanation:
The slope is the number being multiplied by x
Find all the zeros. Write the answer in exact form. c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24
The exact form of the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24 are x=-4, x=-3/2, x=2, and x=1.
To find all the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24, we need to find the values of x that make c(x)=0. One way to do this is by using the Rational Root Theorem, which states that if a polynomial has rational zeros, then they must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
The factors of the constant term, 24, are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24. The factors of the leading coefficient, 3, are ±1 and ±3. Therefore, the possible rational zeros are ±1, ±2, ±3, ±4, ±6, ±8, ±12, and ±24.
Using synthetic division, we can test these possible zeros to see if they are actually zeros of the polynomial. After testing, we find that the zeros are -4, -3/2, 2, and 1.
So, the exact form of the zeros of the polynomial function c(x)=3x^(4)-2x^(3)-39x^(2)-10x+24 are x=-4, x=-3/2, x=2, and x=1.
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The value of y varies directly with x. When y = 1.5, x = 5. What is the value of y when x is 30?
variables y = 1.5, x = 5, hence, the value of y is 9 when x is 30
How are linear equations solved?Two variables, such as x and y, are proportional to one another and their ratio is constant when they vary directly. In other words, if y and x vary directly, their relationship can be written as y = kx, where k is the proportionality constant. With the knowledge that y = 1.5 when x = 5 as provided, we can utilise this information to find the value of y when x equals 30:
1.5 = k(5) \sk = 1.5/5 \sk = 0.3
We can use the equation y = kx to get the value of y for x = 30 now that we know the value of k:
y = 0.3(30) \sy = 9
Hence, the value of y is 9 when x is 30.
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Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned
food collection goal is represented by the expression 7x? - 4xy + 6. The friends have already collected
the following number of cans:
Jessa: 2x2
Tyree: 3x2 - 4
Ben: 3xy + 6
Part A: Write an expression to represent the amount of canned food collected so far by the three
friends. Show all your work. (5 points)
Part B: Write an expression that represents the number of cans the friends still need to collect to meet
their goal. Show all your work. (5 points)
Answer: Your welcome!
Step-by-step explanation:
Part A: 2x^2 + 3x^2 - 4 + 3xy + 6 + 6 = 7x^2 - 4xy + 6
Part B: 0 = 7x^2 - 4xy + 6 - (2x^2 + 3x^2 - 4 + 3xy + 6 + 6)
= 0 = 5x^2 - 4xy
A) The expression that represents the amount of canned food collected by the three friends is [tex]5x^2 + 3xy + 2[/tex].
B) The expression that represents the number of cans the friends still need to collect to meet their goal is [tex]2x^2 - 7xy + 4[/tex].
Given: Number of cans collected
Jessa: 2x²
Tyree: 3x² - 4
Ben: 3xy + 6
Goal : [tex](7x^2 - 4xy + 6)[/tex]
A) The total amount collected:
Total = Jessa + Tyree + Ben
= [tex]2x^2 + (3x^2 - 4) + (3xy + 6)[/tex]
= [tex]2x^2 + 3x^2 - 4 + 3xy + 6[/tex]
= [tex](2x^2 + 3x^2 + 3xy) + (-4 + 6)[/tex]
= [tex]5x^2 + 3xy + 2[/tex]
Therefore, the expression is [tex]5x^2 + 3xy + 2[/tex].
B) The number of cans the friends still need to collect to meet their goal is
Cans still needed = Goal - Total
[tex]= (7x^2 - 4xy + 6) - (5x^2 + 3xy + 2)[/tex]
[tex]= 7x^2 - 4xy + 6 - 5x^2 - 3xy - 2[/tex]
[tex]= (7x^2 - 5x^2) + (-4xy - 3xy) + (6 - 2)[/tex]
[tex]= 2x^2 - 7xy + 4[/tex]
Therefore, the expression is [tex]2x^2 - 7xy + 4[/tex].
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The cost for an 8th grade party isv$450 for a room rental, entertainment, and decorations, plus $20 per person for food. Tickets for the party are sold $25. What is the break-even point?
The break-even point is 45 tickets.
Describe Algebraic Expression?Algebraic expressions can include one or more variables, which are typically represented by letters, such as x, y, or z. These variables can be used to represent unknown quantities or to express relationships between different quantities in a problem.
Algebraic expressions can also include constants, which are fixed numbers, and coefficients, which are the numbers that multiply the variables in the expression. For example, in the algebraic expression 3x + 2y, the constants are 3 and 2, and the coefficients are 3 and 2, respectively.
To find the break-even point, we need to determine the number of tickets that need to be sold in order to cover the costs of the party.
Let's start by setting up an equation to represent the total cost of the party as a function of the number of tickets sold:
Total Cost = Room Rental + Entertainment + Decorations + Food Cost - Ticket Sales Revenue
Total Cost = 450 + 20n - 25n
where n is the number of tickets sold.
Simplifying this equation, we get:
Total Cost = 450 - 5n + 20n
Total Cost = 15n + 450
Now, we need to set the total cost equal to the revenue from ticket sales:
15n + 450 = 25n
Subtracting 15n from both sides, we get:
450 = 10n
Dividing both sides by 10, we get:
n = 45
Therefore, the break-even point is 45 tickets. If the organizers sell 45 tickets, the revenue from ticket sales will cover the total cost of the party, including the room rental, entertainment, decorations, and food cost.
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Alex has a pile of two pence coins. She swapped exactly half of them for the same number of 10p coins. Now she has £4.20. How much money did Alex have initially?"
Alex initially had 60 two pence coins.
What is Algebra?Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. It is used to solve problems and represent mathematical relationships and formulas. In algebra, letters and other symbols are used to represent numbers and quantities, allowing us to express mathematical relationships and patterns in a more general and abstract way.
What is Simplification?In mathematics, simplification refers to the process of reducing an expression or equation to a simpler form. This is typically done by applying mathematical operations or rules to the expression or equation to eliminate unnecessary terms, factors, or operations.
For example, if we have the expression (x^2 + 4x + 4)/(x + 2), we can simplify it by factoring the numerator and canceling out the common factor with the denominator. This gives us (x + 2), which is a simplified form of the original expression.
In the given question,
Let's start by using some algebra to solve the problem.
Let's say that Alex initially had x two pence coins. After swapping half of them for 10p coins, she would have x/2 ten pence coins. We can use this information to set up an equation relating the value of her coins to the total amount of money she ended up with:
0.02x + 0.10(x/2) = 4.20
Simplifying this equation, we get:
0.02x + 0.05x = 4.20
0.07x = 4.20
x = 60
So Alex initially had 60 two pence coins. Checking our answer, we can see that she swapped half of them for 30 ten pence coins. The value of her 60 two pence coins is 0.02 x 60 = £1.20, and the value of her 30 ten pence coins is 0.10 x 30 = £3.00. Together, these add up to £4.20, as required.
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Find a basis of the subspace ofR4defined by the equation3x1−9x2+2x3−3x4=0
The basis of the subspace of R4 defined by the equation3x1−9x2+2x3−3x4=0 is {(3, 1, 0, 0), (-2/3, 0, 1, 0), (1, 0, 0, 1)}
A basis of the subspace of R4 defined by the equation 3x1−9x2+2x3−3x4=0 can be found by solving the equation for one of the variables in terms of the others and then writing the general solution as a linear combination of vectors.
First, solve the equation for x1 in terms of the other variables:
3x1 = 9x2 - 2x3 + 3x4
x1 = 3x2 - (2/3)x3 + x4
Next, write the general solution as a linear combination of vectors:
(x1, x2, x3, x4) = (3x2 - (2/3)x3 + x4, x2, x3, x4)
= x2(3, 1, 0, 0) + x3(-2/3, 0, 1, 0) + x4(1, 0, 0, 1)
Finally, the basis of the subspace is the set of vectors that make up the linear combination:
{(3, 1, 0, 0), (-2/3, 0, 1, 0), (1, 0, 0, 1)}
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(1 point) Lelv1=−123−3,v2=16−4−4,v3=−1640Are the vectorsv1,v2andv3linearly independent? If the vectors are independent, enter zero in every answer blank since zeros are only the values that make the equation below true. If they are dependent, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer.000=−123−3+16−4−4+−1640
v1, v2, and v3 are linearly independent
Yes, the vectors v1, v2, and v3 are linearly independent.
To verify this, we can set up the equation:
a1v1 + a2v2 + a3v3 = 0
If the vectors are linearly independent, then the only way to solve this equation is if a1 = a2 = a3 = 0.
Substituting the values for v1, v2, and v3 into the equation yields:
-123 - 3a1 + 16 - 4a2 - 4a3 - 1640a3 = 0
Solving for a1, a2, and a3, we get:
a1 = 0, a2 = 0, a3 = 0
Therefore, the vectors v1, v2, and v3 are linearly independent.
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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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A factory manufactures a metal peice in 32 minutes new technology allowed the factory to cut that time by 8% then another improvement cut the time by 5% how long does it take to manufacture the peice now round your answer to nearest minute
The time is takes to manufacture the piece after two improvements is 28 minutes
Calculating how long it takes to manufacture a pieceFrom the question, we are to calculate how long it takes to manufacture a metal piece
First, we need to find the new time taken to manufacture the metal piece after the two improvements.
The first improvement reduces the time by 8%. This means that the new time is:
32 - (8% of 32)
= 32 - 2.56
= 29.44 minutes
The second improvement reduces the time by 5%. This means that the new time is:
29.44 - (5% of 29)
= 29.44 - 1.45
= 27.99 minutes
We can round this to the nearest minute, which gives us 28 minutes.
Hence, it takes 28 minutes to manufacture the metal piece.
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help me complete this and i will mark brainlirst
Answer:
Step-by-step explanation:
The method to find the midpoint of two points is (a + b)/2 a and b both being x+x and y+y for the differentiating coordinates respectively.
here, it would be x = (-2 + 4)/2 and y = (5-5)/2
giving you the coordinate [ 1 , 0 ]
How does lowering interest rates by a government’s central bank affect the economy?
Lowering interest rate by a government's central bank can have a significant impact on the economy, as it affects the cost of borrowing money for businesses and individuals, as well as the return on savings and investments.
Lowering interest rate reduces the cost of borrowing money, making it easier for businesses and individuals to access credit. It can also encourage consumers to spend more money, as they may have more disposable income due to lower borrowing costs or higher investment returns.
It can also lead to increased inflation, as businesses and individuals have more money to spend and demand for goods and services increases and reduced returns on savings and investments, which can discourage people from saving and lead to more spending
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Graph Y=2x on this chart thanks
Answer:
Step-by-step explanation:
The slope is 2 so rise / run = 2 / 1, or up two right one.
Please help, Progress reports for the semester coming out soon!!
(Look at screenshot) <33
Answer:
The graph will be parallel with x-axis and intersects y at -8
Step-by-step explanation:
For the function y = -8, whatever the x is, y is always -8.
x y
-10 8
-9 8
-3 8
-2 8
2 8
The graph will be parallel with x-axis and intersects y at -8
