Questian 14 (1 point) A solid metal prism has square base with sides of 4 inches, and height of 6 inches: A hole in the shape of a cylinder; with radius of inch, is drilled through the entire length of the rectangular prism. What is the approximate volume of the remaining solid, in cubic inches? 19 cubic inches 77 cubic inches 96 cubic inches 93 cubic inches 6 In
The approximate volume of the remaining solid is 77 cubic inches.
To find the approximate volume of the remaining solid, we need to subtract the volume of the cylinder from the volume of the rectangular prism.
Step 1: Find the volume of the rectangular prism
- Formula for the volume of a rectangular prism is V = lwh (length × width × height)
- The base of the prism is a square, so l = w = 4 inches
- The height is 6 inches, so V = 4 × 4 × 6 = 96 cubic inches
Step 2: Find the volume of the cylindrical hole
- Formula for the volume of a cylinder is V = π\(r^2\)h
- The radius of the cylinder is 1 inch (1/2 × 2), and the height is 6 inches (same as the height of the rectangular prism)
- V = π × \(1^2\) × 6 = 6π cubic inches (approximately 18.85 cubic inches)
Step 3: Subtract the volume of the cylinder from the volume of the rectangular prism
- Remaining volume = 96 - 18.85 ≈ 77.15 cubic inches.
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Wich is the solution for -7x > 49 ?
Answer:
x > -7
Steps -
-7x > 49
Multiply both sides by (-1) (Reverse inequality)
(-7x) (-1) < 49 (-1)
Simplify
7x < -49
Divide both sides by 7
7x/7 < -49/7
Simplify = x > -7
$1200 are invested for three years at 6% compound interest.
a) How much is the investment worth at the end of three years?
b) How much interest has been earned?
Answer:
I think its A 1200
Step-by-step explanation:
f ( x ) = − x 2 − 12 Find f ( − 3 )
Answer:
f(-3)=-21
Step-by-step explanation:
f(x)=-x2-12
f(-3)=-(-3)2-12
f(-3)=-9-12
f(-3)=-21
Answer:
-3
Step-by-step explanation:
x=-3 substitute in the equation
+3 squared-12=-3
Work out the missing numbers:
a) 18.6 divided by something = 0.02
\(\frac{18.6}{x} =0.02\) X is the "something" in this problem
\(x=\frac{18.6}{0.02}\)
\(x=930\)
Hope this helped :)
Identify whether each statement is true or false
A. All relations are functions,but not all functions are relations
B. All functions are relations, but not all relations are functions
C. In any set of ordered pairs,the second coordinate is called the domain
D. A function is a relations between a set of inputs and a set of outputs with the property that each input is related to exactly one output
The given statements A, B, C, and D are false, false, false, and true, respectively.
A. All relations are functions if, and only if, each element in the domain is related to exactly one element in the range. This means that for all x in the domain, there must be one, and only one, y in the range such that (x,y) is an element of the relation.
B. For a function, each element in the domain is related to exactly one element in the range. This means that for all x in the domain, there must be one, and only one, y in the range such that (x,y) is an element of the function.
C. In any set of ordered pairs, the first coordinate is called the domain.
D. A function is a relation between a set of inputs and a set of outputs with the property that each input is related to exactly one output. This means that for all x in the domain, there must be one, and only one, y in the range such that (x,y) is an element of the function.
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Find the Function and Solution in 2 different parts.
e.g.: Function ║ Solution
y = \(3x^{2}\) + 17 when x = -2
==========================================================
Explanation:
We replace every copy of x with -2. From there, use PEMDAS to simplify
y = 3x^2 + 17
y = 3(-2)^2 + 17
y = 3(4) + 17
y = 12 + 17
y = 29
Therefore, x = -2 pairs up with y = 29.
Put another way, the point (x,y) = (-2, 29) is on the function curve.
HELP ASP!!❤️
WILL GIVE BRAINLIEST!...
Find the slope of the line. Enter your answer in simplest form.
Answer:
\(m=\frac{-4}{3}\)
General Formulas and Concepts:
Order of Operations: BPEMDASSlope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)Step-by-step explanation:
Step 1: Define
Point (-6, 5)
Point (3, -7)
Step 2: Find slope m
Substitute: \(m=\frac{-7-5}{3-(-6)}\)Simplify: \(m=\frac{-7-5}{3+6}\)Subtract/Add: \(m=\frac{-12}{9}\)Simplify: \(m=\frac{-4}{3}\)Answer:
the slope is -4/3
Step-by-step explanation:
m=y2-y1/x2-x1
-7-5=(-12)
3-(-6)=9
-12/9
-12/3=(-4)
9/3=3
-4/3
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The balance of Stephanies average balance checking account at the beginning of last cycle was $200 and the only transaction for the cycle was a check that Stephanie wrote for $100 which cleared exactly halfway through the cycle on what amount did Stephanies checking account pay interest last cycle
Answer: $150
Step-by-step explanation:
From the question, we are informed that the balance of Stephanies average balance checking account at the beginning of last cycle was $200 and that the only transaction for the cycle was a check that Stephanie wrote for $100 which cleared exactly halfway through the cycle.
Since the $100 check was cleared halfway, the amount that Stephanies checking account will pay interest last cycle will be for us to deduct half of $100 from $200. This will be:
= $200 - 1/2($100)
= $200 - $50
= $150
These two polygons are similar.
4
2
9
16
15
w
w = [? ]
45 points asap for anyone who can answer
Ron and Jim are making sandwiches for a party why makes two times as many sandwiches as gym together they make a total of 42 sandwiches which equation can be softer find J the number of sandwiches Jim makes?
14 sandwiches are made by Jim for the event.
Let's write J for the quantity of sandwiches Jim makes.
The information provided indicates that Ron prepares 2J sandwiches, or twice as many sandwiches as Jim.
They create 42 sandwiches altogether.
We can set up the equation: to determine the equation that best captures this circumstance.
J + 2J = 42
By combining similar phrases, we get:
3J = 42
We multiply both sides of the equation by three to separate out J:
J = 42 / 3
When we look at the positive side of the equation, we discover:
J = 14
Jim thus prepares 14 sandwiches for the gathering.
In conclusion, the number of sandwiches prepared by Jim and Ron is represented by the equation J + 2J = 42,
where J is the quantity of sandwiches manufactured by Jim.
We can find Jim produces 14 sandwiches for the party by calculating the equation.
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(125,75)-(40,72) işleminin sonucunu bulunuz
85,03 çevap budur inşallah doğrudur iyi dersler
A rental car company charges $77. 50 per day to rent a car and $0. 14 for every mile
driven. Juan wants to rent a car, knowing that:
• He plans to drive 425 miles.
• He has at most $230 to spend.
Write and solve an inequality which can be used to determine d, the number of days
Juan can afford to rent while staying within his budget.
77.5d + .14m
m = 425
.14 * 425 = 59.5
77.5d + 59.5 ≤ 230
77.5d ≤ 170.5
d ≤ 170.5/77.5
d ≤ 2.2
if they only take payment for whole days, he has 2 whole days
during a huge snowstorm in the White Mountains last year it snowed 66.5 cm in one day how much did it snow in meters?
Answer: It snowed 0.665 meters
hope this helps! :)
Answer:
Step-by-step explanation:
61.5cm= (6.15/100)m = .615m
The new cylinder can has a radius of 5cm and a height of 9cm how many centimeters of aluminum will it take to make this new cylinder can
Answer:
439.8 cm²
Step-by-step explanation:
The new cylinder can has a radius of 5cm and a height of 9cm how many centimeters of aluminum will it take to make this new cylinder can
We are to find the Total Surface Area of this cylinder
The formula is given as:
A=2πrh+2πr²
A =2× π × 5 ×9 + 2 × π × 52
= 439.82297 cm²
Approximately = 439.8 cm²
It would take 439.8 square centimeters of aluminum to make this cylindrical can
Prove that if x^3 is irrational then x is also irrational. First write a proof on your own and then put the following statements into order to obtain the proof. 1. Put N next to the 4 statements that should not be used in the proof. 2. Thus, x^3 = c/f, and by definition of rational x^3 is rational. 3. By definition of rational, there exist integers a, b notequalto 0 such that x = a/b. 4. By definition of rational, there exist real numbers a, b notequalto 0 such that x = a/b. 5. Since a and b are integers, e = a^3 and f = b^3 is also an integer. 6. Therefore, if x is rational then x^3 is rational, or equivalently if x^3 is irrational then x is irrational. 7. Since the cube of a fraction is a fraction x^3 is rational. 8. Suppose x is an arbitrary rational number. 9. By definition of rational, there exist a b notequalto 0 such that x = a/b. 10. Suppose x^3 is an arbitrary irrational number. 11. Then, x^3 = a^3/b^3.
This statement is true, and if \(x^3\) is irrational then x is also irrational. N: 2, 7, 8, 9.The proof that if \(x^3\)is irrational, then x is also irrational can be demonstrated by contradiction.
Suppose that x is a rational number, meaning that there exist integers a and b not equal to 0 such that x = a/b. Then,\(x^3 = a^3/b^3\), and since the cube of a fraction is a fraction, \(x^3\) is rational. Thus, by definition of rational, there exist real numbers c, f not equal to 0 such that\(x^3\) = c/f. Therefore, if x is rational then \(x^3\) is rational, or equivalently if\(x^3\) is irrational then x is irrational. Thus, this statement is true, and if \(x^3\) is irrational then x is also irrational. N: 2, 7, 8, 9.The proof that if \(x^3\) is irrational, then x is also irrational can be demonstrated by contradiction.
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Carlos uses a food delivery service to order lunch. He paid $13.75 for lunch, which included the cost of the food and a delivery fee, which is 10% of cost of the food. What was the cost of Carlos' lunch before the delivery fee? Enter your answer in the box.
Answer:
$12.50
Step-by-step explanation:
Let x = the cost of the food without the delivery fee.
The delivery fee can be represented as 0.10x.
Keep in mind that the cost of the food plus the delivery fee equals $13.75.
Therefore, your equation will look like: 13.75 = x + 0.10x
x + 0.1x = 1.10x
So, 13.75 = 1.10x
This means that x = 13.75/1.10
x = 12.5 = $12.50
Answer: Let's represent the cost of the food as "x".
We know that the delivery fee is 10% of the cost of the food, so it can be written as 0.1x.
The total cost that Carlos paid for lunch is the sum of the cost of the food and the delivery fee, which is:
Total cost = Cost of food + Delivery fee
$13.75 = x + 0.1x
Simplifying the equation, we get:
$13.75 = 1.1x
Dividing both sides by 1.1, we get:
x = $12.50
Therefore, the cost of Carlos' lunch before the delivery fee was $12.50.
YES 12.50 is correct I am a k12 student and I have proof. the quiz name is 2.09 Quiz: Multistep Percent Problems
Evaluate 3^2 + (7 - 2) x 4 -6/3
Answer:
Answer:
Step-by-step explanation:
find an equation of the tangent line to the curve at the given point. y = x4 + 5x2 − x, (1, 5)
The equation of the tangent line to the curve y = x^4 + 5x^2 - x at the point (1, 5) is y = 13x - 8.
To find the equation of the tangent line to the curve y = x^4 + 5x^2 - x at the point (1, 5), we need to find the derivative of the curve at that point, which will give us the slope of the tangent line.
Taking the derivative of y = x^4 + 5x^2 - x, we get:
y' = 4x^3 + 10x - 1
Plugging in x = 1 (since we want the tangent line at the point (1, 5)), we get:
y' = 4(1)^3 + 10(1) - 1 = 13
So the slope of the tangent line at (1, 5) is 13. To find the equation of the tangent line, we use the point-slope form of a line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the point we're given (in this case, (1, 5)). Plugging in m = 13 and (x1, y1) = (1, 5), we get:
y - 5 = 13(x - 1)
Expanding and simplifying, we get:
y = 13x - 8
So the equation of the tangent line to y = x^4 + 5x^2 - x at the point (1, 5) is y = 13x - 8.
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I WILL MARK YOU BRANLIEST IF YOU ANSWER THIS QUESTION
9^-1/2 and 27^-2/3 what is this
Answer:
9^(-1/2) = 1/3
27^(-2/3) = 1/9
Step-by-step explanation:
We know that:
\( \displaystyle \large {{a}^{ - n} = \frac{1}{ {a}^{n} } } \\ \displaystyle \large { {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } }\)
If we add negative sign in m/n.
\( \displaystyle \large{ {a}^{ - \frac{m}{n} } = \frac{1}{ {a}^{ \frac{m}{n} } } }\)
Therefore,
\( \displaystyle \large{ {a}^{ - \frac{m}{n} } = \frac{1}{ \sqrt[n]{ {a}^{m} } } }\)
From the expression:
1. 9^(-1/2)
\( \displaystyle \large{ {9}^{ - \frac{1}{2} } = \frac{1}{ \sqrt{9} } }\)
From above, apply the exponent rules. Simplify the expression:
\( \displaystyle \large{ {9}^{ - \frac{1}{2} } = \frac{1}{ 3 }}\)
2. 27^(-2/3)
\( \displaystyle \large{ {27}^{ - \frac{2}{3} } = \frac{1}{ \sqrt[3]{ {27}^{2} } } }\)
27 can be factored as 3^3.
\( \displaystyle \large{ {27}^{ - \frac{2}{3} } = \frac{1}{ \sqrt[3]{ { ({3}^{3}) }^{2} } } }\)
From above:- Use the following exponent rules to multiply the exponents and leave the base as 3 so we can cancel the cube (3 out of the root) and the exponent.
\( \displaystyle \large{ {27}^{ - \frac{2}{3} } = \frac{1}{ \sqrt[3]{ {3}^{6} } }}\)
Divide 6 by 3 or the cube root.
\( \displaystyle \large{ {27}^{ - \frac{2}{3} } = \frac{1}{ {3}^{2} }}\)
Therefore:
\( \displaystyle \large{ {27}^{ - \frac{2}{3} } = \frac{1}{ 9}}\)
Translate this phrase into an algebraic expression, Nine more than the quotient of a number and 7 is 6
Answer:
x/7 + 9 = 6
Step-by-step explanation:
Hope this helps! Please give brainliest!
The perimeter (distance around the shape) of a rectangle is 40 cm. The length is 14 cm.
Let x = width of the rectangle.
Ravi says he can find the width using the equation 2(x + 14) = 40.
Fran says she can find the width using the equation 2x + 28 = 40.
Answer the questions to solve the equations and to compare the steps and solutions.
2. What would your next step be?
A. Add 14 to both sides
B. Subtract 14 from both sides
C. Divide both sides by 2
D. Multiply both sides by 2
Answer:
D. D is your answer.
Step-by-step explanation:
D is your answer because 2 is right next to the parentheses. Multiply. If this is wrong, I am so sorry. I really am, but that's what I got.
Hope this helps!
Sincerely,
Josiah Kumai
hello I need help on this; graph the linear function p(x)=4x
Answer:
I hope this helps
Explanation:
Write the expression using an exponent.
1·7·7·7·7·7
Answer:
7⁵
Step-by-step explanation:
An exponent indicates how many times a number multplies itself.
Examples:
2² = 2* 2
2⁴ = 2 * 2 * 2 * 2
Yadira'smom is buying hot dogs and hot dog buns for the family barbecue.
Hot dogs come in packs of 12 and hot dog buns come in packs of 9.
The store does not sell parts of a pack and Yadira's mom wants the same
number of hot dogs as hot dog buns.
What is the smallest total number of hot dogs that Yadira's mom can
nurchase?
Step-by-step explanation:
To find the smallest total number of hot dogs that Yadira's mom can purchase, we need to find the least common multiple (LCM) of 12 and 9, since she wants the same number of hot dogs as hot dog buns.
The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...
The least common multiple of 12 and 9 is 36, since it is the smallest number that appears in both lists. Therefore, Yadira's mom should purchase 36 hot dogs (3 packs of 12) and 36 hot dog buns (4 packs of 9) for the family barbecue.
a knowledge of statistics helps us make decisions based on ______ evidence.
Empirical, A knowledge of statistics is essential for anyone who wants to make informed decisions based on empirical evidence.
A knowledge of statistics helps us make decisions based on empirical evidence. Empirical evidence is data that has been collected through observation and experimentation, and statistics is a method for analyzing and interpreting this data. By using statistical tools and techniques, we can draw conclusions from empirical evidence and make informed decisions based on this information.
Statistics plays a crucial role in modern society, from medicine and public policy to business and finance. A knowledge of statistics enables individuals to understand and analyze data, to make informed decisions based on empirical evidence, and to communicate findings to others. Statistics helps us to quantify uncertainty and variability, to identify patterns and trends, and to make predictions based on past data. By using statistical methods, we can determine the probability of certain outcomes, assess risks and benefits, and evaluate the effectiveness of interventions or policies. For example, in medical research, statistics is used to test the effectiveness of new treatments or therapies, to determine the safety of drugs, and to identify risk factors for diseases. In public policy, statistics is used to analyze demographic trends, to assess the impact of social programs, and to inform decision-making around issues such as climate change or public health.
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Solve for x.
4x = 36
x = [?]
Answer:
Step-by-step explanation:
4x is in a multiplication form
4x=36
meaning a number when multiplied with 4 gives the answer 36
hence in order to find the answer
36 divided by 4 which is equivalent to 9
answer is 9
Answer: \(x = 9\)
Step-by-step explanation:
We must isolate \(x\) on one side of the equation in order to solve the equation \(4x = 36\) for \(x\).
Step 1: Divide both sides of equation by 4:
\(\frac{4x}{4} = \frac{36}{4}\)
Step 2: Simplify
\(x = 9\)
Therefore, the solution to the equation is \(x = 9\).
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FAQWhat does isolating x mean?Rearranging an algebraic equation so that \(x\) is on one side and all other terms are on the other side of the equal sign is known as isolating \(x\).
Write an equation in the form y=kx for the relationship shown in the graph.
Answer:
y=6.5x
Step-by-step explanation:
Choose a point on the graph and tell what the point represents.
The point (2, 13) represents the height of the balloon after 2 seconds.
What is the constant of proportionality?
Because
height
time
=
13
2
= 6.5, the constant of proportionality is 6.5.
Write an equation in the form y = kx.
y = 6.5x
The equation is y = 6.5x.
What is equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.
We can consider the point (24, 6)
To write the value of K we can write
=24/6
= 4
Hence, the equation is y=4x.
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Multiplying Polynomials Multiple Choice
Need to know what goes in blanks and final answer
PLEASE HELP
\((5 x + 1)( {x}^{2} + 8x + 3) \\ 5 {x}^{3} + 40{x}^{2} + 15x + {x}^{2} + 8x + 3 \\ 5 {x}^{3} + 41 {x}^{2} + 23x + 3\)
hope it helps you ❣❣
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