The time it would take Amal to run 1 mile if he maintains the pace is 12 minutes
From the question, we are to determine how long it would take Amal to run 1 mile
From the given information,
Amal can run 1\8 mile in 1 1\2 minutes.
First, we will calculate Amal's speed
Using the formula,
Speed = Distance/ Time
Then,
Amal's speed = 1/8 ÷ 1 1/2
Amal's speed = 1/8 ÷ 3/2
Amal's speed = 1/8 × 2/3
Amal's speed =1/12 miles/minute
Now, we will determine how long it would take him to run 1 mile
Time = Distance/ Speed
Time = 1 ÷ 1/12
Time = 1 × 12/1
Time = 12 minutes
Hence, the time it would take Amal to run 1 mile if he maintains the pace is 12 minutes
Here is the complete question:
Amal can run 1\8 mile in 1 1\2 minutes. If Amal can maintain that pace, how long will it take him to run 1 mile.
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A computer is rendering two scenes. The computer has already rendered 540 thousand pixels (\text{kpx}kpxstart text, k, p, x, end text) of a kitchen scene and renders another 90\,\text{kpx}90kpx90, start text, k, p, x, end text each minute. The computer has rendered 960\,\text{kpx}960kpx960, start text, k, p, x, end text of a garden scene and renders 60\,\text{kpx}60kpx60, start text, k, p, x, end text more pixels each minute. After how many more minutes will the scenes have the same amounts rendered?
The minutes when the scenes have the same amounts rendered is 14 minutes.
How to illustrate the expression?The expression for the kitchen is illustrated as 540 + 90t.
The expression for the garden is illustrated add 960 + 60t.
Therefore, for the same amount, this will be:
540 + 90t = 960 + 60t.
Collect like terms
90t - 60t = 960 - 540
30t = 420
Divide
t = 420 / 30
t = 14 minutes
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Which point is a solution to the following system of inequalities? "-2x+3y>=1" "-5x+6y<=1"
a. (6,6)
b. (7,8)
c. (8,7)
d. (9,7)
By option verification,
i.e., substituting the options by given equation and verifying
Given -2x + 3y > = 1 and - 5x + 6y <= 1
Substituting option A i.e., ( x , y ) = ( 6,6)
-2x + 3y >=1 --> -2 * 6 + 3 * 6 >= 1
--> -12+ 18 >= 1
---> 6>=1
-5x + 6y<=1--> -5 * 6 + 6 *6 <=1
--> -30+ 36 <=1
-->6<=1
False
Substituting option B i.e., (x , y)= (7 ,8)
-2x + 3y>=1 --> -2* 7 + 3 * 8>=1
--> -14 + 24>=1
--> 10>=1
-5x + 6y<=1 --> -5 *7 + 6* 8<=1
--> -35 + 48<=1
--> 13<=1
False
Substituting option C i.e., (x, y) = ( 8 ,7)
-2x + 3y >=1 --> -2* 8 + 3* 7>=1
--> -16 + 21>=1
--> 5>=1
-5x + 6y <=1 --> -5 * 8 + 6 * 7 <=1
--> -40 + 42<=1
--> 2<=1
False
Substituting option D i.e., (x ,y ) = (9, 7)
-2x + 3y >= 1 --> -2* 9 + 3 * 7 >=1
--> -18 +21>=1
--> 3>=1
-5x + 6y <=1 --> -5* 9 + 6 * 7 <=1
--> -45 + 42<=1
--> -3<=1
True
Therefore (x ,y ) = (9, 7) is the solution of the given equation -2x + 3y>=1 and -5x = 6y <=1
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Answer: For the people who were just as confused with the answer above, the answer is D-
Step-by-step explanation:
8 1/2 - 4 2/3?????????
let's firstly convert the mixed fractions to improper fractions and then subtract.
[tex]\stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{17}{2}} ~\hfill \stackrel{mixed}{4\frac{2}{3}}\implies \cfrac{4\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{14}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{17}{2}~~ - ~~\cfrac{14}{3}\implies \stackrel{\textit{using the LCD of 6}}{\cfrac{(3)17~~ - ~~(2)14}{6}}\implies \cfrac{51~~ - ~~28}{6}\implies \cfrac{23}{6}\implies {\LARGE \begin{array}{llll} 3\frac{5}{6} \end{array}}[/tex]
Solve for y 2y - x = 34 (-y + 1)
The solution for y is given as : y = (34+x)/36
According to the question we have been the linear equation in two variable as :
2y - x = 34 (-y + 1)
We need to solve the above equation for y. For that we will do step by step.
First we will open the brackets on the right hand side of the equation we get
2y - x = -34y + 34
then we will combine the terms on the left hand side of the equation.
2y + 34y = 34 + x
36y = 34+x
dividing both the sides by 36 we get
36y/36 = (34+x)/36
y = (34+x)/36
Hence the solution for y is given as : y = (34+x)/36
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Based on the diagram, which of the following statements must be true?
A. No lines are parallel
B. a || b and l || m
C. l || m
D. a || b
Answer: The answer is B. a||b and l||m
Step-by-step explanation: I hope this helps.
Find f(4) when f(x) = x 2-3x + 3
Step-by-step explanation:
f(x) = x² - 3x + 3
f(4) = 4² - 3.4 + 3
f(4) = 16 - 12 + 3
f(4) = 7
what is 37x1000 plases help
Answer:
Step-by-step explanation: 37 times 1000 equals 37000 if you times anything by 1000 just add 2 zeros to the end
Giving 80 points to the person who answers correctly
The function f(t) represents water going into a swimming pool with respect to the number of hours(t) water is flowing in where(t) represents time. f(t)=t squared +8t+9 There is a leak in the pool and it’s losing water at a rate represented by d(t). d(t)=t squared +11t+4
a.Write a function w(t) to represent the amount of water in the pool using the two functions.
b. Use the new function to determine if the pool will leak all of the water
c. If the pool will drain of all water, how much time will it take?
d.Will f(t) and d(t) intersect on a graph? Explain what it means if they do.
e. What is the domain of f(t), d(t), and w(t)? Explain your answer.
Using operations with functions, we have that:
a) w(t) = -3t + 5.
b) The pool will leak all the water in 1.67 hours.
c) 1.67 hours.
d) Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.
e) The domain of the function is 0 ≤ t ≤ 1.67.
What is the amount of water in the pool?The amount of water in the pool is determined by the subtraction of the amount flowing into the pool by the amount being drained out the pool.
For this problem, these following functions are given:
Flowing: f(t) = t² + 8t + 9.Draining: d(t) = t² + 11t + 4.Hence the amount of water in the pool is given by:
w(t) = f(t) - d(t)
w(t) = t² + 8t + 9 - t² - 11t - 4
w(t) = -3t + 5.
Hence:
The function is: w(t) = -3t + 5.
The pool will have leaked all the water when:
w(t) = 0.
Hence:
-3t + 5 = 0.
3t = 5
t = 1.67.
The pool will leak all the water in 1.67 hours.
Equaling f(t) and d(t), we have that:
t² + 8t + 9 = t² + 11t + 4.
3t = 5.
t = 1.67.
Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.
The domain of a function is the set that contains all input values of the function. For this problem, the input is the time, hence:
Time cannot be negative, hence t ≥ 0.When all the water has been drained, everything stops, hence t ≤ 1.67.Hence:
The domain of the function is 0 ≤ t ≤ 1.67.
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What is 4÷139 as a decimal answer ?
Please help me.
Answer:
0.025
Step-by-step explanation:
Divide 4 by 139 and get the number as a decimal
Drew is an artist. He paints portraits. The table below shows the number of portraits painted in hours. What is the constant of proportionality?
The constant of proportionality for the paints portraits is estimated as 5.
What is defined as the constant of proportionality?When two variables are proportional to one another, their relationship can be expressed as y = kx or y = k/x, in which k defines how the two factors are connected to one another. This k is recognized as the proportionality constant.The proportionality constant is the fixed value of the ratio of two proportional quantities. When the ratio or product of two varying quantities yields a constant, they are said to be in a proportional relationship.For, the given question;
The relation between the portraits and the time for their drawing made by Drew is-
In 5 hours ----> 1 portrait
Thus, 5/1 = 5
In 10 hours ------> 2 portrait
Thus, 10/2 = 5
In 15 hours -----> 3 portrait
Thus, 15/3 = 5 .....and so on.
Therefore, the constant of proportionality is found as 5.
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the different between 8 and 4,divided by 2
Answer:
2
Step-by-step explanation:
8-4=4
4/2=2
Answer:
so you take 2×4=8 and 2×2=4 I think that's how to do it
What is the radius of D
A. 6 cm
B. 12 cm
C. 3 cm
D. 24 cm
Help me ASAP!
90x - 128 = 24x + 50
Greetings from Brasil...
90X - 128 = 24X + 50
90X - 24X = 50 + 128
X = 89/33A square picture with an area of 100 cm² is mounted on a square piece of matting. The matting has 2.5 times the area of the picture. If the picture is centred on the matting, what width of matting is visible around the outside of the picture? Give your answer to the nearest tenth of a centimetre.
150cm² is the area of matting visible.
What exactly are mathematical operations?An operation, also known as an "operand" or "argument," is a mathematical function that converts zero or more input values into a precisely defined output value.The arity of the operation is influenced by the number of operands.Unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, and binary operations (i.e., operations of arity 2), such as addition and multiplication, are the operations that are most frequently studied.A constant is an operation of arity zero, also known as a nullary operation.The mixed product serves as an example of a ternary operation, which is an operation of arity 3.So, the area of matting is 100 × 2.5:
100 × 2.5 = 250cm²Now, the area of the matting is visible:
250 - 100 = 150cm²Rounding to nearest tens: 150cm²
Therefore, the area of matting visible is 150cm².
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Which equation does not belong with the other three? Explain your reasoning.
²³/x+ ²/3=y\
y = 0.5x -0.2
4x + 3 = y
y = x² +6
:: a linear equation
does not belong because it is
while the other three equations are
:: y = 0.5x -0.2 :: 4x +3=y :: y = x² +6
:: not a linear equation
:: not linear equations
x + = y
3/
:: linear equations
Answer:
3 = x ÷ 4
Step-by-step explanation:
Given expressions:
8 = x - 2 ⇒ x = 8 + 2= 10
3 = x ÷ 4 ⇒ x = 3*4 = 12
x - 6 = 5 ⇒ x = 5 + 6 = 11
x - 3 = 9 ⇒ x = 9 + 3 = 12
3 of them involves addition, one of them - multiplication
The second expression doesn't belong
Which of the following is equivalent to
(p3)(2p^2 - 4p)(3p^2 - 1)?
A.(p3)(6p^4 - 12p^3 - 2p^2 + 4p)
B.(p3)(6p^4 + 4p)
C.(2p^6 - 4p^3)(3p^2 - 1)
D.(2p^5 - 4p^4)(3p^5 - p^3)
The equivalent expression is (p3)(6p^4 - 12p^3 - 2p^2 + 4p).
what is expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given:
(p^3)(2p^2 - 4p)(3p^2 - 1)
Now further solving
(p^3)(2p^2 * 3p^2 - 2p^2 * 1 - 4p * 3p^2 + 4p)
=(p^3) (6p^4 - 2p^2 - 12 P^3 + 4p)
=(p3)(6p^4 - 12p^3 - 2p^2 + 4p)
Hence, the value of expression is (p3)(6p^4 - 12p^3 - 2p^2 + 4p).
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What did i do wrong here
Answer: Everything lol
Step-by-step explanation:
How do I write this out and answer it right
The numeric values of the expressions are given as follows:
3. 36.
5. 38.
7. 16/61.
How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
In item 3, we have that:
4|m - n|, m = -7, n = 2.
Hence the numeric value is:
4|-7 - 2| = 4|-9| = 4 x 9 = 36.
In item 5, we have that:
s²t - 10 with s = -8, t = 3/4.
Hence the numeric value is:
(-8)² x 3/4 - 10 = 48 - 10 = 38.
In item 7, we have that:
(a + b)^5/(a - 2b²), a = 6, b = -8.
Hence the numeric value is:
(-2)^5/(6 - 128)
-32/-122 (negative divided by negative is positive).
32/122 (simplify by 2).
16/61.
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find the quotient of (−2/9)÷(−2 1/3÷1/9).
Answer: 2/189
Step-by-step explanation:
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C of t is equal to the quantity negative 18 times t squared plus 54 times t end quantity over the quantity t squared plus 7 times t plus 10 end quantity comma where the time, t is hours after injection.
Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations.
The domain of the function C(t) is R - { -5. -2}.
What is a domain?The domain of a function is the set of all values for which the range of the function is defined.
To achieve an immediate response to a particular drug's effects the concentration, C, in mg/L, of a particular medication after being injected into a patient is given by the function
C(t) = [tex]\frac{-18t^2 + 54t}{t^2 + 7t + 10}[/tex] where t represents time in hours.
We know that a function is undefined when its denominator becomes zero.
∴ We have to factor the quadratic equation t² + 7t + 10 which is,
t² + 5t + 2t + 10 = 0.
t(t+5)+2(t+5) = 0.
(t+5)(t+2) = 0.
So, t = -5 or t = -2 are the two values of this equation which makes the function c(t) undefined.
∴ The domain of the function [tex]\frac{-18t^2 + 54t}{(t+5)(t+2)}[/tex] is all real numbers except -2 and - 5 which can be written as
Domain of C(t) is R - { -5, -2}, where R represents all real numbers.
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Can u help me mates Like im dum
Answer:
U: (-7, 0)
S: (-7, -2)
T: (3, -2)
Step-by-step explanation:
Moving a point 6 to the left is the same as subtracting 6 from its x value. Moving a point up 1 is the same as adding 1 to its y value.
Point=(x-6, y+1) where x is the point's original x value and y is the point's original y value.
U: (-1-6, -1+1)=(-7, 0)
S: (-1-6, -3+1)=(-7, -2)
T: (9-6, -3+1)=(3, -2)
Please help very quickly
The name of each midpoint and the segment it bisects include the following:
Point R bisects line segment PQ.Point X bisects line segment WY.Point Y bisects line segment WZ.Point D bisects line segment CA.What is a line segment?A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.
How to determine the midpoint of a line segment?In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
In this scenario, the name of each midpoint and the segment it bisects include the following:
Point R bisects line segment PQ.Point X bisects line segment WY.Point Y bisects line segment WZ.Point D bisects line segment CA.Read more on midpoint and line segments here: https://brainly.com/question/28367319
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Complete Question:
Name each midpoint and the segment it bisects.
Solve the equation for a.
−7(a+13)=−6(−3a+10)
a=
Answer:d=-3743
Step-by-step explanation:
Mrs. White ordered 6 large boxes and 9 small boxes of crayons for the school art classes. Each large box has 189 crayons, and each small box has 90 crayons. Which is the best estimate of the number of crayons Mrs. White ordered
help me please i need to know how to do this
Answer:
12'
Step-by-step explanation:
Pythagoras theorem = a² = b²+c²
*a² is always the hypothenuse (the longest side if the triangle)
you could use b² as the base and c² as the height
to find the height i.e., c² you transpose and substitute what we know so that'll be
13'² = 5'² + c²
you expand which will then give you
169 = 25 + c²
you then take over the 25+ which when addition goes over the equal sign becomes subtraction so that'll now give you
169 - 25 = c²
144 = c²
we want to find for c not c² so to do that we find the square root of 144 which is equal to 12.
so the height is equal to 12'
hope this helps
Tonya is paid a salary of $650 a month at her sales job. She also earns a commission on her sales in this way: 3% on all sales up to $32,000 in a month
and 8% on all higher sales. What were Tonya's total earnings for a month where her total sales were $80,000?
Tonya's total earnings for a month where her total sales were $80,000 is $5,450
What made up Tonya's total earnings?
Tonya's total earnings in any month comprises the basic salary of $650 , 3% of sales as sales commission on sales revenue of up to $32,000 and 8% as commission on sales in excess of $32,000
total earnings=basic salary+(3%*sales of up to $32,000)+(8%*sales of above $80,000)
basic salary=$650
3%*sales of up to $32,000=3%*$32,000
3%*sales of up to $32,000=$960
8%*sales of above $80,000=8%*($80,000-$32,000)
8%*sales of above $80,000=8%*$48,000
8%*sales of above $80,000=$3,840
Tonya's total earnings for a month=$650+$960+$3,840
Tonya's total earnings for a month=$5,450
Note that the total earnings based on the basic salary of $650 and sales revenue of $80,000 is $5,450
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determine the probabilities of being dealt each of the following hands from a poker deck of 52 cards. a.) three cards all of the same type. b.) four cards all of a different type (no pairs, three of a kind or four of a kind). c.) six cards of which exactly four are of the same suit.
A) 54,912 B) 2,598,960 C) 15
A) The number of ways to produce three of a kind (Num3) is equal to the product of the number of ways to make each independent choice. Therefore,
Num3 = 13C1 * 12C2 * 4C3 * 4C1 * 4C1
Num3 = 13 * 66 * 4 * 4 * 4 = 54,912
B) First, we count the number of five-card hands that can be dealt from a standard deck of 52 cards. This is a combination problem. The number of combinations is n! / r!(n - r)!. We have 52 cards in the deck so n = 52. And we want to arrange them in unordered groups of 5, so r = 5. Thus, the number of combinations is:
52C5 = 52! / 5!(52 - 5)! = 52! / 5!47! = 2,598,960
Hence, there are 2,598,960 distinct poker hands.
C) 6 C 4 = 6! / 4! (6-4)!
= 6*5*4! / 4!*2!
= 30 / 2
= 15
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what number can equal 2x² -50=
The number that can be equal to 2x² -50 = 2(x + 5)(x - 5).
What is defined as the quadratic equation?A quadratic equation has a single factor of degree two. It has the general form ax² + bx + c = 0,, at which x is the variable, a, b, and c are constants, and a = 0.This same standard form of a quadratic equation is given to us in the question as - ax² + bx + c = 0,When we compare the statement in the question to the definition discussed above, we can conclude that the given statement is correct. The standard form of the a quadratic equation is ax² + bx + c = 0,, where a, b, and c are constant real numbers. The constant 'a' cannot be zero as it will indeed reduce the degree of the equation to one.For the given equation;
= 2x² -50
Take 2 common;
= 2(x² - 25)
This could be written as;
= 2(x² - 5²)
Now use per the property of (a² - b²) = (a + b)(a - b).
= 2(x + 5)(x - 5)
Thus, the given expression 2x² -50 can be represented as 2(x + 5)(x - 5).
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I need help! Thank you
Solve each equation. Check your answers. ln x=-2
After solving the equation ln x = -2, x is the value of equal to [tex]e^{-2}[/tex]
We have been asked to find x in ln x = -2
⇒ ln x = -2
⇒ x = [tex]e^{-2}[/tex]
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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