Find the volume of the bath tub by multiplying all the dimensions together:
18 inches = 1.5 feet:
5 ft x 3 feet x 1.5 feet = 22.5 cubic feet.
The tub is 3/4 full so multiply the volume by 3/4 to find the amount of water in the tub:
22.5 x 3/4 = 16.875 cubic feet of water.
The tub drains at 1 cubic foot per minute, so it would take about 17 minutes to drain. (16.875 rounded to the nearest whole minute).
crate a list of steps, in order, that will solve the following equation. 2(x+3/4)^2 -5 =123
Answer:
x = -8.75; x = 7.25
Step-by-step explanation:
2(x + ¾)² - 5 = 123
Add 5 to each side: 2(x+ ¾)² = 128 Divide each side by 2: (x+ ¾)² = 64 Take the square root of each side: x + ¾ = 8 x + ¾ = -8 Subtract ¾ from each side: x = 8 - ¾ x = -8 - ¾ Convert to decimal fraction: x = 8 - 0.75 x = -8 – 0.75 Subtract: x = 7.25 x = -8.75The graph of your equation is a parabola with x-intercepts at x = -8.75
and x = 7.25.
The list of steps, in order, that will solve the equation is:
Addition of 5 to both sides to eliminate the value of -5Division of both sides of the equation by 2 to eliminate the coefficient of 2 from the left-hand sideTaking the square root of both sidessubtract 3/4 from each sideConvert the answer to decimalThe given expression is raised to a power of 2, so we can say that the given expression is a quadratic equation.
What is a quadratic equation?A quadratic equation is a form of an algebraic expression in which the variable is usually raised to the power of its second degree.
From the parameters given:
[tex]\mathbf{2(x + \dfrac{3}{4})^2 -5 = 123 }[/tex]
Addition of +5 to both sides[tex]\mathbf{2(x + \dfrac{3}{4})^2 -5 +5 = 123+5 }[/tex]
[tex]\mathbf{2(x + \dfrac{3}{4})^2 = 128}[/tex]
Division of both sides by 2[tex]\mathbf{\dfrac{2(x + \dfrac{3}{4})^2 }{2} =\dfrac{ 128}{2}}[/tex]
[tex]\mathbf{(x + \dfrac{3}{4})^2 = 64}[/tex]
Taking the square root of both sides[tex]\mathbf{\sqrt{(x + \dfrac{3}{4})^2} =\sqrt{ 64}}[/tex]
[tex]\mathbf{(x + \dfrac{3}{4})} =\pm8}[/tex]
Subtract 3/4 from both sides[tex]\mathbf{(x + \dfrac{3}{4} - \dfrac{3}{4}) }\mathbf{= \pm 8-\dfrac{3}{4}}[/tex]
[tex]\mathbf{x= \pm 8-\dfrac{3}{4}}[/tex]
[tex]\mathbf{x= +8-\dfrac{3}{4} \ \ OR \ \ x= -8-\dfrac{3}{4}} [/tex]
[tex]\mathbf{x=7.25 \ \ OR \ \ -8.75} [/tex]
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Divide (x^3-8x^2+17x-10)/(x-5)
Answer:
(x - 2)*(x - 1) is the answer
Step-by-step explanation:
We have to divide the polynomial f(x) = x^{3}-8x^{2}+17x-10 by (x-5).
Now, after dividing f(x) gets simplified into (x-5)*(x^{2}-3x+2).
So, we need to factorize the quadratic equation x^{2}-3x+2.
i.e. x^{2} - 3x + 2 = x^{2} - x - 2x + 2 = x(x-1) - 2(x-1) = (x - 2)*(x - 1)
Therefore, f(x) again gets simplified into (x-5)*(x - 2)*(x - 1)
Now eliminating the common factor (x-5).
We get, [tex]\frac{x^{3}-8x^{2}+17x-10}{x-5}[/tex] = (x - 2)*(x - 1)
Answer:
[tex]x^{2}-3x+2[/tex]
Step-by-step explanation:
Use synthetic division.
Reverse the sign of -5 and write the coefficients of the polynomial.Multiply the coefficient by the divisor, then add to the next coefficient.Continue through the last coefficient.5 | 1 -8 17 -10
+ 5 -15 10
1 -3 2 0
The quotient is [tex]x^{2} -3x+2[/tex].
PLEASE HELP!!!!! THANK YOU!
Answer:
The slope is found by the change in Y over the change in x.
Using the given points:
The change in Y = -8 - 4 = -12
The change in x = 2 - -6 = 2 +6 = 8
The slope is -12/8
Both the numerator and denominator can be divided by 4
-12/4 = -3
8/4 = 2
The slope = -3/2
Natasha is observing the growth of a population of bacteria. She started out with 250 bacteria cells. The population of bacteria quadruples every hour. Use x to represent the number of hours and y to represent the population of the bacteria. Enter an equation that represents this scenario in the box.
Answer:
[tex]y=250(5)^x[/tex]
Step-by-step explanation:
The growth of a population of bacteria can be represented by exponential growth function,
[tex]y=a(1+r)^x[/tex]
where,
y = the population of the bacteria after x hours,
x = the number of hours,
a = initial population of bacteria,
r = rate of growth,
At the beginning the number bacteria was 250 and the population of bacteria quadruples every hour i.e rate of growth is 400% or 4 per hour.
Putting all the values,
[tex]y=250(1+4)^x[/tex]
[tex]\Rightarrow y=250(5)^x[/tex]
Suppose f(x)=x2 Find the graph of f (x)+1
You would vertically shift the function up a unit, making it clear that the answer should be graph 3.
Use the image below, red is the original function, and blue is the new function.
Solve using substitution
x=2y-6
y= -3x+17
Answer:
(x, y) = (4, 5)
Step-by-step explanation:
given the 2 equations
x = 2y - 6 → (1)
y = - 3x + 17 → (2)
Either substitute x = 2y - 6 into (2) or y = - 3x + 17 into (1)
substituting y = - 3x + 17 into (1)
x = 2(- 3x + 17) - 6
x = - 6x + 34 - 6
x = - 6x + 28 ( add 6x to both sides )
7x = 28 ( divide both sides by 7 )
x = 4
substitute x = 4 into (2)
y = - 12 + 17 = 5
solution is (4, 5 )
Jasmine arrives at school at 7am. She starts the day with 9 sharpened pencils. She asks Kim to sharpen pencils. Kim sharpens eleven pencils every minute for the next seven mins. What was the number of sharpened pencils at 7:07 am?? Plz I will give you 100 points
Answer:
should be about 86
Step-by-step explanation:
multiply 11 by seven and then add nine because thats what you had originally.
we multiply because in those seven minutes we're constantly adding more pencils so instead of adding, multiplication is the easiest to do
9+(7x11)
you get to pick 8 of your 12 favorite songs to put on a cd . how many ways 8 songs be arranged from a choice of 12 songs
Three snacks bars contain 1/5,0.22, and 19 percent of their Calories from fat. Which snack bar contains the least amount of calories from fat?
Answer:
19 percent
Step-by-step explanation: First we need to convert them all the a similar format. Fractions would be easiest.
.22 = 22/100
1/5 = 20/100
19% = 19/ 100
The one that contains the least is 19/100 or 19%.
Considering only functions with a greater rate of change than that of the function represented on the graph, which function has the lowest rate of change? (only one answer)
A) y = 13/7x - 7/3
B) y = 7/5x + 2/5
C) y = 11/8x + 3/8
D) y = 5/4x + 13/4
E) y = 5/3x - 8/3
Answer:
C (1.38)
Step-by-step explanation:
The graphed function has the slope 4/3, which is obvious: As x increases from 0 to 1.5, y increases from -2 to 0. Thus, m = rise / run = 2/1.5 = 4/3.
Which of the given functions have greater rates of change than 4/3? These include A (1.86), B (1.4), C (1.38), E (1.67). Of these, C has the lowest rate of change (1.38).
The lowest rate of change of the function is y = 11/8x + 3/8. The correct option is C.
What is a function?
The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
The graphed function has a slope of 4/3, which is obvious: As x increases from 0 to 1.5, y increases from -2 to 0. Thus, m = rise / run = 2/1.5 = 4/3.
Which of the given functions has greater rates of change than 4/3? These include A (1.86), B (1.4), C (1.38), E (1.67). of these, C has the lowest rate of change (1.38).
Therefore, the lowest rate of change of the function is y = 11/8x + 3/8. The correct option is C.
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What is the measure of angle c in the diagram below?
A. 105°
B. 137°
C. 16°
D. 121°
At the beginning of the week Fayez writes down the mileage of his limo at 2529 at the end of the week the mileage is 2834, Fayez knows he used 75.2 litres of petrol during this week. The handbook states the limo uses 1 gallon of petrol for every 20 miles. Fayez wants to know if his limo uses 1 gallon of petrol for every 20 miles that week. 1 gallon = 4.54 litres . Did his limo use 1 gallon of petrol every 20miles that week. Show your answer clearly
Answer:
No. It used 1 gallon in 18.41 miles.
Step-by-step explanation:
He travelled 2834 - 2529 = 305 miles.
So his consumption is 305 / 75.2 = 4.056 miles/litre.
This equals 4.056*4.54 = 18.41 miles / gallon.
So this is less than the 1 gallon every 20 miles stated by the handbook.
Answer: His limo used 1 gallon fuel for 18.4136 miles.
Step-by-step explanation:
Fayez covered distance:
2834 - 2529 = 305 miles.
He used fuel = 75.2 litres
75.2/4.54 = 16.5638 gallons petrol used.
His limo covered distance / total petrol used = 305 miles / 16.5638 gallons petrol = 18.4136 miles per gallon.
That is less than 20 miles per gallon
Alicia runs for exercising falicia runs 8 Miles and 6 days how many days will it take for her to run 36 miles
Alicia runs 8 miles in 6 days. By setting up a proportion, it's calculated that it will take her 27 days to run 36 miles at the same rate.
Calculating Days Needed to Run a Total Distance:
Alicia runs 8 miles in 6 days. To find out how many days it will take her to run 36 miles, we can set up a proportion. Since the number of days is directly proportional to the miles run, we can use the equation:
8 miles / 6 days = 36 miles / x days
By cross-multiplying, we get:
8 miles * x days = 6 days * 36 miles
x = (6 days * 36 miles) / 8 miles
The miles cancel out, leaving us with:
x = 216 / 8
x = 27 days
Therefore, it will take Alicia 27 days to run a total of 36 miles if she continues running at the same rate.
Brian works 40 hours a week. He spends 40% of his time helping customers, 13% doing paperwork, and the remainder performing other store tasks. What percentage of Brian's time is spent on other store tasks?
40% helping customers + 13% doing paper work = 53% of his time.
This means 100% - 53% = 47% of his time he is doing other tasks.
Two runners start 30 kilometers apart and run toward each other. They meet after 3 hours. One runner runs 2 kilometers per hour faster than the other runner. What rate do they run?
2 km/hr and 4 km/hr
3 km/hr and 5 km/hr
5 km/hr and 7 km/hr
4 km/hr and 6 km/hr
Answer: 4 km/hr and 6 km/hr
Step-by-step explanation:
A runner = 4km/hr
A runner covered distance after 3 hours = 12 km
B runner = 6km/hr
B runnet covered distance after 3 hours = 18 km
Total distance = 12 + 18 = 30km
When solving for x what would (8x-46) + (10x-8)
Answer:
18x - 54 :) :( :) :)What is the remainder when the polynomial f(x)=3x^3-4x^2+2x+8 is divided by (x-5)
Answer:
remainder = 290
Step-by-step explanation:
[tex]\frac{3x^3-4x^2+2x+8}{x-5}[/tex]
= 3x² + 11x + 57 + [tex]\frac{290}{x-5}[/tex]
quotient = 3x² + 11x + 57 and remainder = 290
How many batches of soup can Marcia make
Answer:
400 divided by 5 is how you get the answer.
Step-by-step explanation:
400 / 5 = 80
80 batches of soup.
Linda received a $ 90 gift card for a coffee store. She used it in buying some coffee that cost $ 7.63 per pound. After buying the coffee, she had $ 51.85 left on her card. How many pounds of coffee did she buy?
Answer:
5 pounds
Step-by-step explanation:
:'>
Answer:
She bought 5 pounds of coffee.
Step-by-step explanation:
Please answer with calculations
Answer:
Step-by-step explanation:
Given that a storage rack has dimensions as 25x12x5 ft.
Box has dimensions as 15x8x10 inches
Volume of each box = 15(8)(10) = 1200 inches = 1200x12^(-3) feet^3
Volume of 5000 boxes = 5000 (1200x12^(-3) ) = 3472.22 cubic feet
Volume of storage rack = 25(12)(5) = 1500 cubic feet
Volume of 25 storage racks 1500(25) = 37500 cubic feet.
SInce storage racks have sufficient volume it is concluded that enough storage is there.
Answer:
Yes, we have enough storage space.
Step-by-step explanation:
25 storage racks that are:
Length: Lsr = 25 ft = 25 ft (12 in / 1 ft) → Lsr = 300 in
Width: Wsr = 3 ft = 3 ft (12 in / 1 ft) → Wsr = 36 in
Height: Hsr = 12 ft = 12 ft (12 in / 1 ft) → Hsr = 144 in
5000 boxes 15x8x10 in
Length: Lb = 15 in
Width: Wb = 8 in
Height: Hb = 10 in
In the length of each storage rack we can put:
Nl=Lsr/Lb=300 in / 15 in → Nl = 20
In the width of each storage rack we can put:
Nw=Wsr/Wb=36 in / 8 in = 4.5 → Nw = 4
In the height of each storage rack we can put:
Nh=Hsr/Hb=144 in / 10 in = 14.4 → Nh = 14
Then we can put in each storage rack:
N = Nl Nw Nh = (20)(4)(14) → N=1,120 boxes
And we have 25 storage racks, then we can storage in total:
Nt=25N=25(1,120)→Nt=28,000 boxes
And we have 5,000 boxes, then we have enough storage space
You are making sets of pens and pencils to sell. You want each set to contain the same combination of pens and pencils. You have 28 pens and 80 pencils, and you want to use them all. What is the greatest number of these sets you can make?
The greatest number of sets of pens and pencils that can be made, using all of the given 28 pens and 80 pencils in each set, is 4. Each set would contain 7 pens and 20 pencils.
Explanation:In the problem, we are looking to find the Greatest Common Divisor (GCD), which is the greatest number that can evenly divide both the number of pens (28) and the number of pencils (80). The GCD between 28 and 80 is 4.
Thus, the most sets of pens and pencils you can make would be equal to the GCD, which in this case is 4.
This means you can put together 4 sets with an equal number of pens and pencils in each set. In each of these sets, there would be 7 pens (28 pens ÷ 4 sets) and 20 pencils (80 pencils ÷ 4 sets).
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Final answer:
To maximize the number of sets with 28 pens and 80 pencils, find the greatest common divisor and divide the total by it. You can create 27 sets of 4 pens and 10 pencils each.
Explanation:
To find the greatest number of sets you can make with 28 pens and 80 pencils, you need to determine the highest common factor of the two quantities.
Calculate the greatest common divisor (GCD) of 28 and 80, which is 4.
Divide the total number of pens and pencils by the GCD: (28 + 80) ÷ 4 = 27.
You can make 27 sets, each consisting of 4 pens and 10 pencils.
a jewelry store makes 5 dollar profit for each 1 dollar they spend on jewelry. a jewelry store owner made a profit of 95 dollars on a necklace. what was the original cost of the necklace? solve by using equivalent ratios.
solve and simplify, typing the final answer as a fraction 1/4 ÷ 3/8
[ Answer ]
2 / 3
[ Explanation ]
1 * 8 / 4 * 3
8 / 12
Simplify:
2 / 3
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How do u write 10 x10x10x10 using exponents
Answer: I'm not really sure how to shrink the number to the top but in word form it would be 10 to the power of 4.
At the art fair, 95 artists exhibited their work. Of those 95 artists, 25 showed sculptures and 48 showed paintings. If 12 showed both sculptures and paintings, how many artists showed only sculptures or paintings?
To determine the number of artists who showed only sculptures or paintings at the art fair, we use the formula for the principle of inclusion-exclusion, resulting in 61 artists.
Explanation:To find out how many artists showed only sculptures or paintings at the art fair, we apply the principle of inclusion-exclusion. First, we add the number of artists who showed sculptures (25) to those who showed paintings (48), which gives us a total of 73 artists. However, this counts the 12 artists who showed both sculptures and paintings twice, so we subtract 12 from this total to correct for the double counting. Therefore, the number of artists who showed only sculptures or paintings is 73 - 12, which equals 61 artists.
7/8 & -8/7 are these line slope perpendicular or parallel or neither
Answer:
Perpendicular!
Step-by-step explanation:
If they were parallel they would have the exact same slope. If they are perpendicular their slopes would be opposite reciprocals of each other... which they are. Another trick to tell if two slopes are perpendicular is to multiply them by each other and if the answer equals -1 they are perpendicular:
7/8 • -8/7 = -1/1 = -1
Write an algebratic expression for "six more than the quantity d times two."
Answer:
6+2d
Step-by-step explanation:
An algebraic expression for 'six more than the quantity d times two' is written as 2d + 6, which represents the multiplication of d by two, followed by the addition of six.
To write an algebraic expression for "six more than the quantity d times two," you first perform the multiplication and then add six.
The quantity d times two is expressed as 2d. Then, to represent "six more" than this quantity, you add six to the product, which is written as [tex]2d + 6[/tex].
i dont understand this help me :( What is the equation of a line with a slope of 3 and a point (3, 1) on the line?
Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{1})~\hspace{10em} slope = m\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=3(x-3) \\\\\\ y-1=3x-9\implies y=3x-8[/tex]
Answer please ?!?!?!
Answer: -9
Step-by-step explanation: -91/6 ≈ -9.167
21/3 ≈ 2.33333
-17/8 ≈ -1.875
-9.167 + 2.3333 + -1.875 = -8.71
Rounded, the answer is -9.
A plane travels at a constant speed. It takes 6 hours to travel 3,360 miles
To find the average speed of the plane, divide the total distance traveled, which is 3,360 miles, by the total time of the journey, which is 6 hours, resulting in an average speed of 560 miles per hour.
Explanation:The student's question involves calculating average speed, which is a concept in Physics, specifically within the topic of kinematics. To find the average speed of the plane you would use the formula:
average speed = total distance / total time
In this case, the plane travels 3,360 miles in 6 hours, so the calculation would be:
average speed = 3,360 miles / 6 hours = 560 miles/hour
This calculation demonstrates how to determine the average speed of an object in motion when given the total distance traveled and the total time taken. This concept is analogous to determining the average speed in other examples, such as a car journey or a train trip.