The time they would both meet at the starting point is 140 minutes (third option).
When would they meet at the starting point?The time they would both meet at the starting point will be a common multiple of the time it takes each of them to complete a lap.
A multiple of a number is the product of an integer and that number. A common multiple is a multiple that is common to two or more numbers.
Multiple of 20 = 20, 40, 60, 80, 100, 120, 140
Multiple of 35 = 35, 70, 105, 140, 175
Lowest common multiple of 20 and 35 = 140
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A car can be rented for $95 per week plus $0.20 per mile. How many miles can be driven if you have at most $370 to spend for weekly transportation?
Answer:
1375 miles
Step-by-step explanation:
0.20x+95=370
0.20x=275
x=1375
An ice cream factory makes 100 quarts of ice cream in 5 hours. How many quarts could be made in 36 hours?
Answer:
They can make 720 quarts in 36 hours.
Step-by-step explanation:
First we set up a ratio of 100 quarts:5 hours since that is a given ratio. Since hours was in the denominator of the ratio before, we place the 36 in the denominator of the other ratio, x quarts: 36 hours.
Setting them equal gives the following proportion:
100/5=x/36
Cross multiply to solve:
5x=3600
x=720
Answer:
720
Step-by-step explanation:
100 divided by 5 =20 and 20 times 36 is 720 hope this helped
X(2x-5) = 12
How to solve for x?
Answer:
[tex]x=4,\:x=-\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]x\left(2x-5\right)[/tex]
Apply the distributive law.
[tex]=x\cdot \:2x-x\cdot \:5[/tex]
[tex]=2x^2-5x[/tex]
[tex]2x^2-5x=12[/tex]
Subtract 12 from both sides.
[tex]2x^2-5x-12=12-12[/tex]
[tex]2x^2-5x-12=0[/tex]
Now, apply the quadratic formula.
[tex]x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:2\left(-12\right)}}{2\cdot \:2}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-5\right)\pm \:11}{2\cdot \:2}[/tex]
Separate the solutions.
[tex]x_1=\frac{-\left(-5\right)+11}{2\cdot \:2},\:x_2=\frac{-\left(-5\right)-11}{2\cdot \:2}[/tex]
Simplify.
[tex]x=4,\:x=-\frac{3}{2}[/tex]
Find the equation of the given table in slope intercept form. Please show work, answer must be in y=mx+b format!
Answer:
y=5x+1.5
Step-by-step explanation:
First, we need to find the slope which is M
put B as 0 for now so we going to plug in 2 numbers on the same horizontal side
I'm going to use (-2 and 11.5) and (4 and -18.5), and now I'm going to do [tex]\frac{y^{2}-y^{1} }{x^{2} -x^{1} } \\[/tex] which -18.5-11.5/4-(-2)
I'm going to get 30/6 which means 5
the slope is 5 now we can find Y-intercept by plugging in a pair of Y and X and plug in M to find B
11.5=(5)-2+b
11.5=10+b now we going to separate b by subtracting 10 from both sides
1.5=b
Simplify 2x+x+x+2y×3y×y
Answer: 6y^3 +4x
Step-by-step explanation:
collect like terms
2x + x + x + 2y * 3y *y
so
6y^3 +4x
Answer:
6y3 + 4x ( 3 is cube)Step-by-step explanation:
2x + x + x + 2y ( 3 )yy
2x + x + x + 6y 3
Combine Like Terms:2x + x + x + 6y3
( 6y3 ) + ( 2x + x + x)
6y3 + 4x
Part of your bathroom remodel involves you needing to repaint. the walls measure to be 150 square feet. if a gallon of paint covers 400 square feet, how many gallons do you need to buy if you need 2 coats?
I need to buy 0.75 gallons of paint 2 coats on the wall.
We are given the area of wall, which is 150 square feet. So, if I need to put double or two coats on the wall, the area of wall to be considered will be : 150 × 2
Area of wall to be considered = 300 square feet
As per the information on paint -
400 square feet is covered by amount of paint = 1 gallon
300 square feet will be covered by amount of paint = (1 ÷ 400) × 300
Amount of paint = 300 ÷ 400
Amount of paint = 0.75 gallons
Therefore, I need to buy 0.75 gallons of paint 2 coats on the wall.
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whats 9 and 4 exponent time negative 1/3 and 4 exponent?
1. 1.371742E−3
2. 256 .
What is an Exponent?
An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 2³) means: 2 x 2 x 2 = 8.
It is written as a small number to the right and above the base number.
Here in the question we find out (9)∧-3 and (4)∧4
1. (9)∧-3 =x∧n=9−1
x∧n=9-³
=1/9³
=1/9×9×9
=1/729
=0.0013717421124829
=1.371742E−3
2. (4)∧4 =x∧n=4∧4
=4×4×4×4
=256
The meaning of exponent is a symbol written above and to the right of a mathematical expression to indicate the operation of raising to a power.
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Trying to prepare a budget, alvin has done research and found that he spends an average of $123 on his phone/internet/cable service, $213 on his electric bill, and $270 on his health insurance premium. if he earns $2600 per month, estimate the amount of money he will have after paying these bills each month.
A alvin makes 3,200 and spends 701 each month leaving 2,499.
What are average?The average can be calculated by dividing the sum of observations by the number of observations.
Average = Sum of observations/the number of observations
It is Given that alvin has done research and found that he spends an average of $123 on his phone/internet/cable service, $213 on his electric bill, and $270 on his health insurance premium.
Subtract expenditures from earnings;
= 3200 - (178 + 203 + 320)
= 3200 - 701
= 2499
Thus, Grant will have $2,499 after paying these bills each month
Therefore, alvin makes 3,200 and spends 701 each month leaving 2,499.
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What are the units on each side of the equation gmm/x2 = mv2/x? (m and m are two different masses.)
In the given statement is:
Gravitational Force between two bodies at a distance x is given by:-
F = GmM/ x2 ; If a body of mass ' m' is revolving around the body of mass M and it's orbit is stationary then centrifugal force must be equal to the Gravitational Force i.e. Fg = mv2/x therefore FG = Fg i.e. GmM/ x2 =mv2/x; where v is the orbit motion of the orbiting body of mass.
Now, Let us understand the :
In mechanics, gravity, often known as gravitation, is the constant force of attraction occurring on all matter. It plays no part in shaping the interior features of common stuff because it is easily the weakest force known to exist in nature.
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What are all the solutions for the inequality m> −9?
m=3
m= −20
m= −12
m= −2
Answer:
m = [-9, +infinity]
Step-by-step explanation:
he zeros of a quadratic function are 6 and -4. Which of these choices could be the function?
A.
f(x) = (x + 6)(x + 4)
B.
f(x) = (x + 6)(x − 4)
C.
f(x) = (x − 6)(x + 4)
D.
f(x) = (x − 6)(x − 4)
Answer:
The answer is option C
Step-by-step explanation:
The roots of the quadratic equations are x= 6 or x= -4
X-6=0 or x+ 4=0
⇒(x-6)(x+4)
F(x)=(x-6)(x+4)
A zumba instructor charges according to the number of participants. If there art 15 participants or below, the instructor charges 500.00 for each participant per month. If the number of participants is between 15 and 30 , he charge 400.00 for each paetricipants pe month . If there are 30 partricipantsor more . he charge 350.00 for each partricipas per month
The piecewise function that describes what the instructor charges is; f(x) = 500x , 0 < x ≤ 10
400x , 10 < x < 25
350x , x ≥ 25
How to create piecewise functions?
Let x represent the number of participants and let y represent the charge per participant.
Now, y depends on x, and as such we can say that;
f(x) = y
For, 0 < x ≤ 10, the total charges is 500x,
f(x) = 500x , 0 < x ≤ 10
For 10 < x < 25, total charge is 400x,
f(x) = 400x , 10 < x < 25
For x ≥ 25, the total charge is 350
f(x) = 350x x ≥ 25
Therefore, we can say that;
f(x) = 500x , 0 < x ≤ 10
400x , 10 < x < 25
350x , x ≥ 25
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Write the piecewise function that describes what the instructor charges.
What are the coordinates of the point on the directed line segment from (-4, 1)(−4,1) to (1, 6)(1,6) that partitions the segment into a ratio of 4 to 1?
Calculate the 95onfidence interval for the true population mean based on a sample with =225, =8.5, and =45. function
The true population mean is (222.52, 227.48) with a 95% confidence interval.
What is the critical factor?The critical factor for a 90% confidence interval for the true population mean is given by;
Critical factor = (x-μ)/(s/√n)
where, x = sample mean repair cost
s = standard deviation of a sample
n = sample of stereos
μ = critical value
⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95
⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95
⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95
95% confidence interval for
⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))
Here, x = 225, s = 8.5, and n = 45
⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))
⇒ μ = (222.52, 227.48)
Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.
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The question seems to be incomplete the correct question would be
Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.
7+2+3 and 3+2+2 are the same?
Associative Property of Addition
Identify the transformation that maps the figure onto itself. A Reflect across the line x = 3 Reflect across the line x = 3, B Rotate 180° about the point (3, -3)Rotate 180° about the point (3, -3) C Rotate 180° about the point (5, -5)Rotate 180° about the point (5, -5) D Reflect across the line y = -3
Answer:
D Reflect across the line y = -3
Step-by-step explanation:
The only way you can divide the trapezoid so that there are two congruent parts is when you draw a line on y=-3.
13
Write the time.
-9
11 12
10
8
76
1
2
Answer:
5:45
...................................
Answer:
the time is 5:45 PM according to that watch
titanium has a density of 4.5g/cm find the volume of a 90g sample
PLEASE HELP ME
Answer:
20cm^3
Step-by-step explanation:
Divide 90 by 4.5.
90/4.5 = 20
We can multiply the density ratio by this quotient in order to find the volume of a sample 20x the size of the ratio's sample.
(4.5 x 20)/(1cm^3 x 20)
90g/20cm^3
In this step, let's identify the clues provided in the questions. We have:
Mass of sample: 90 gramsDensity of sample: 4.5 g/cm³To find: The volume of titaniumSince we know the mass and density of titanium, we can apply the density formula to determine the volume of titanium.
Footnote: I have included the formula in case if you need to know it.
[tex]\boxed{\text{Density} = \frac{\text{Mass (Grams)}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
Step-2) Substituting the given clues into the Density formulaTo work out the volume of the titanium, we need to substitute the given clues from the question, into the formula. We have:
[tex]\text{Density} = \dfrac{\text{Mass (Grams)}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
When we substitute the mass and the density of titanium, we have:
[tex]4.5 \ \text{g/cm}^{3}} = \dfrac{\text{90 grams}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
Step-3) Simplify and solve for volumeFinally, let's simplify the equation.
[tex]4.5 \ \text{g/cm}^{3}} = \dfrac{\text{90 grams}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
[tex]1 \ \text{g/cm}^{3}} = \dfrac{\text{20 grams}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
[tex]\text{Volume (cm}^{3}) = \dfrac{\text{20 grams}}{\text{1 g/cm} ^{3} }[/tex]
[tex]\text{Volume (cm}^{3}) = \dfrac{\text{20 grams}}{\text{1 g/cm} ^{3} } = \dfrac{20 \ \text{grams} \ \times 1 \ \text{cm}^{3} }{1 \ \text{grams}} = \boxed{20 \ \text{cm}^{3}}[/tex]
Therefore, the volume of titanium is 20 cm³.
A farmer has 160 bushels of apples to sell at his roadside stand. he sells an average of 14 7/8 bushels each day represent the total change in the number of bushels he has for sale after 5 days
The change of 74.375 bushels is seen with around 86 bushels remaining with farmer for further sale.
We are given the total number of bushels as 160. Now, the average sale on each day is [tex]14\frac{7}{8}[/tex] bushels.
Converting this mixed fraction into fraction -
Average bushels sold everyday = ((8×14)+7)÷8
Performing multiplication and addition to find average bushels sold each day
Average bushels sold everyday = 119÷8
So, at this rate the total number of bushels sold in five days will be = (119÷8)×5
Performing multiplication and division on Right Hand Side of the equation to find the number of bushels
Total number of bushels sold in five days will be = 74.375
So, after five days of sale, the available number of bushels are 160 - 74.375
Change in number of bushels = 85.62
Rounding off to find the exact number of bushels = 86
Hence, the change of 74.375 bushels is seen with around 86 bushels remaining with farmer for further sale.
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The distance from arias home to the science museum is 0.72 mile which fraction is equivalent to this distance in miles.
The fraction which is equivalent to this distance in 0.72 mile of science museum from Arias home is 18/25.
What is described as a fraction?Fractions are defined as a numerical value that represents a portion of a whole.
A fraction is a portion or section of any quantity taken from the whole, which can be any number, a constant set, or a thing.Every fraction has a numerator or a denominator divided by a horizontal bar recognized as the fractional bar.The denominator represents the number of parts into which the whole has also been subdivided. It is positioned below the fractional bar in the bottom section of the fraction.The numerator specifies how many fractional sections are depicted or selected. It is positioned above the fractional bar in the upper portion of the fraction.For the given question.
The distance from the science museum to Arias home is 0.72 mile.
As, we have to 2 significant figures on the right of the decimal.
Then, remove the decimal and divide the number by 100.
= 72/100
Now, divide the numerator and denominator by 4 , we get;
= 18/25
Therefore, the distance between the Arias home and the science museum in fraction is written as 18/25.
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Danae is choosing between two jobs. One job pays an annual bonus of $1,500 plus $120 per day worked. The second job pays an annual bonus of $2,500 plus $110 per day worked. Which equation can be solved to determine after how many days, d, Danae would make the same amount of money regardless of the job she chooses?
O 120d + 110d = 1,500 + 2,500
O 120 + 110 = 1,500d + 2,500d
• 120d + 1,500 = 110d + 2,500
• 120d + 2,500 = 110d + 1,500
Answer: 120d + 1500 = 110d + 2500
Solution: The first 1500 + 120d
The second 2500 + 110d
So. 120d + 1500 = 110d +2500
Nate and Maya are building model cars. Maya's car is 3 inches less than 2 times the length of Nate's car. The sum of the lengths of both cars is 26 inches. Write an equation to determine the lengths of Nate's and Maya's cars.
x + 3 − 2x = 26
x + 2x = 26
2x − 3 = 26
x + 2x − 3 = 26
Answer:
x + 2x - 3 = 26
Step-by-step explanation:
Define the variables:
Let x = length of Nate's car.Let y = length of Maya's car.If Maya's car is 3 inches less than 2 times the length of Nate's car, then:
⇒ y = 2x - 3
If the sum of the lengths of both cars is 26 inches, then:
⇒ x + y = 26
Substitute the found expression for y into the equation:
⇒ x + y = 26
⇒ x + (2x - 3) = 26
⇒ x + 2x - 3 = 26
Therefore, the equation to determine the lengths of Nate'a and Maya's cars is:
[tex]\boxed{x + 2x - 3 = 26}[/tex]
Solving the equation for x
⇒ x + 2x - 3 = 26
⇒ 3x - 3 = 26
⇒ 3x - 3 + 3 = 26 + 3
⇒ 3x = 29
⇒ 3x ÷ 3 = 29 ÷ 3
⇒ x = 9.7 in (nearest tenth)
Therefore, Nate's car is 9.7 in (nearest tenth).
To find the length of Maya's car, subtract the length of Nate's car from 26:
⇒ 26 - 9.7 = 16.3 in (nearest tenth).
Therefore, Maya's car is 16.3 in (nearest tenth).
Answer:
d) x + 2x - 3 = 26
Step-by-step explanation:
Given that,
→ Maya's car is 3 inches less than 2 times the length of Nate's car.
→ The sum of the lengths of both cars is 26 inches.
Now the equation will be,
→ x - 3 + 2x = 26
→ x + 2x - 3 = 26
→ 3x = 29
Hence, option (d) is correct answer.
Solve the equation p + 5 = −12 for p.
Answer: 17
Explanation
P-5=12
Transpose 5 to the other side
It will become +5 after transposing becuase it was -5 before transposing
P=12+5
P=17
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Two irrational numbers that equal to 2. What are they?
The two irrational numbers that sum up to 2 are (√5 - 2) and (4 - √5)
What are irrational numbers?Irrational numbers are numbers that cannot be expressed or written as a quotient of integers.
Example of irrational numbers are; √5 , √7, √3, etc
Irrational numbers that can add up to 2
(√5 - 2) + (4 - √5)
expand the bracket
√5-2 + 4-√5
collect like terms
√5 - √5 -2 + 4
-2 + 4
2
Hence, the two irrational numbers that sum up to 2 are (√5 - 2) and (4 - √5)
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3. If a = -2 and b = 6, find the value of each of the
following.
ii) 6a - b
i) 2a + b
iii) 3a - 26
v) a +3ab
iv) 4ab
vi) a² + b²
What is the remainder when f(x) = x4 + 7x3 + 17x2 + 20x is divided by x2 + 4?
Answer:/
Step-by-step explanation:
The lengths of the four sides of a
quadrilateral (in inches) are consecutive integers. If
the perimeter is 110 inches, find the value of the longest of the four side lengths.
The value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
According to the given question.
The lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
So, let the length of the quadrilateral be x, (x + 1), (x + 2), and (x + 3).
Also, it is given that the perimeter of the quadrilateral is 110 inches.
⇒ x + x+1 + x + 2 + x + 3 = 110
⇒ 4x + 6= 110
⇒ 4x = 110 -6
⇒ 4x = 104
⇒ x = 104/4
⇒ x = 26 inches
Thereofore, the length of the sides of the quadrilaterals is given by
x = 26 inches
x + 1 = 26 + 1 = 27 inches
x + 2 = 26 + 2 = 28 inches
x + 3 = 26 + 3 = 29 inches
Hence, the value of the longest of the four side length is 29 inches, if the lengths of the four sides of a quadrilateral (in inches) are consecutive integers.
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Find the exact equation of the function graphed to the right. Show your work. Vertex: (-2,4) x intercepts:(-5,0) (1,0) y intercept (0,2)
The equation for the parabola Is; y = -²/₅[(x + 5)(x - 1)]
How to Interpret a Quadratic Graph?
We are given the following;
x-intercepts = (-5,0) and (1,0)
y - intercept = (0, 2)
We know that the x-intercepts are the roots of the quadratic equation while the y-intercept is the value of y when x is zero.
Thus;
(x + 5) and (x - 1) are factors of the given quadratic equation.
f(x) = a(x + 5)(x - 1)
At y-intercept of (0,2), we have;
a(0 + 5)(0 - 1) = 2
a = -2/5
Thus we can write the equation for the parabola as;
y = -²/₅[(x + 5)(x - 1)]
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Attribute data is data that logically can be only whole numbers and can be expressed as:_____.
Attribute data is data that logically can be only whole numbers and can be expressed as control charts.
What is Attribute data?Attribute data is information that is used to create control charts. This information can be used to generate a variety of chart systems, such as percent charts, charts displaying the number of affected units, count-per-unit charts, demerit charts, and quality score charts. In a nutshell, variable data is data in which quality is described quantitatively in terms of dimensions, weights, or other characteristics, whereas attribute data is data in which quality is described qualitatively in terms of measurements. Attribute data examples include sorting and counting the number of blemishes (defects) in a specific product and the number of nonconforming pieces (defectives). Assume we want to look into the quality of a bag of M&Ms.Therefore, attribute data is data that logically can be only whole numbers and can be expressed as control charts.
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Part 1: Mapping Diagrams
Look at the mapping diagrams below, which represent two different relations. The relation on the
left is a function since each value in the blue set is paired with one value in the yellow set. For
the function on the left, the domain is {0, 1, 2, 3) and the range is {0, 1.69, 3.38, 5.07).
1. Is the relation on the right a function? Explain.
20
70
-60
3
-6
2
5
Based on the definition of a function,
1. The relation on the right is not a function.
2. Domain: {20, 70, -60}
Range: {3, -6, 2, 5}
What is a Function?A relation that is defined as a function has each domain value that is assigned to only one possible range value, in such a way that, each of the domain element cannot have two different range element that corresponds to it.
1. The relation on the right has a domain element, -60, which corresponds to two different range element, -6 and 2.
Therefore, the relation on the right is not a function.
2. The domain of the relation that is not a function is: {20, 70, -60}
The range of the relation that is not a function is: {3, -6, 2, 5}
In summary, based on the definition of a function,
1. The relation on the right is not a function.
2. Domain: {20, 70, -60}
Range: {3, -6, 2, 5}
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