Question 9 A cylindrical beaker with a base radius of 3 inches and a height of 11 Inches weighs 3.5 ounces when empty. The beaker is filled with water to one inch from the top. If one cubic Inch of water weighs 0.6 ounce, how many ounces does the beaker weigh, including the weight of the cylindrical beaker? Explain how you found your answer. Round to the nearest tenth.
The weight of the beaker, including the weight of the water, is approximately 173.1 ounces when rounded to the nearest tenth. To find the weight of the beaker when filled with water, including the weight of the cylindrical beaker itself, we need to calculate the weight of the water and add it to the weight of the empty beaker.
First, let's find the volume of the water in the beaker. The beaker is filled to one inch from the top, which means the height of the water is 11 - 1 = 10 inches.
The volume of the water can be calculated using the formula for the volume of a cylinder: \(V = \pi r^2h\), where r is the radius and h is the height.
\(V = \pi (3^2)(10) = 90\pi\) cubic inches
Next, we need to find the weight of the water. Given that one cubic inch of water weighs 0.6 ounces, we can multiply the volume of the water by 0.6 to get the weight of the water.
Weight of water = 90π x 0.6 = 54π ounces
Finally, we need to add the weight of the empty beaker, which is 3.5 ounces, to the weight of the water.
Weight of beaker with water = 54π + 3.5 ounces
To find the approximate value, we can use the value of π as 3.14.
Weight of beaker with water ≈ 54 x 3.14 + 3.5 ≈ 169.56 + 3.5 ≈ 173.06 ounces
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An equation was created for the line of best fit from actual enrollment data. It was used to predict the dance studio enrollment values shown in the table below:
Enrollment
Month
January
February
March
April
May
June
Actual
500
400
550
550
750
400
Predicted
410
450
650
650
600
450
Residual
90
−50
−100
−100
150
−50
Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit. (1 point)
Select one:
a. No, the equation is not a good fit because the sum of the residuals is a large number.
b. No, the equation is not a good fit because the residuals are all far from zero.
c. Yes, the equation is a good fit because the residuals are not all far from zero.
d. Yes, the equation is a good fit because the sum of the residuals is a small number.
The inference from the information is A. No, the equation is not a good fit because the sum of the residuals is a large number.
What is a line of best fit?It should be noted that line of best fit simply means a line through a scatter plot of data points which shows the relationship between the points.
In this case, the inference from the information is that the equation is not a good fit because the sum of the residuals is a large number.
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what is the solution to the equation 5x = -4?
Answer:
x = -4/5
Step-by-step explanation:
Divide 5 on both sides to isolate x on one side. You get x = -4/5
Answer:
x=-4/5 hope this helps you out math is always hard
A construction crew is lengthening a road. The road started with a length of 54 miles, and the crew is adding 3 miles to the road each day.
Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 37 days.
The equation for calculation of total length is L = 54 + 3D and the total length for 37 days 165 miles.
The equation will be formed as total length will be sum of first length travelled with the product of number of miles travelled each day and number of days. Representing this as the equation -
L = 54 + 3D
Now, keep the value of D in formula to find the total length.
L = 54 + 3×37
Performing multiplication on Right Hand Side of the equation
L = 54 + 111
Performing addition on Right Hand Side of the equation
L = 165 miles
Therefore, the equation is L = 54 + 3D and total length is 165 miles.
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The graph of quadratic parent function f was transformed to create the graph of g(x) = f(x + 2) - 5. Which graph best represents g?
Answer:
Step-by-step explanation:
C
Can someone help me with this question please? I really need help and the assignment is already late :(
The image of A after a reflection using the y-axis is (-2, -1).
Given that, the coordinate of point A is (2, -1).
The image of A after a translation 2 units to the right.
Translation rules:
When the shape is moved towards the right by k units, then replace x with x + k.
Here, (2+2, -1)=(4, -1)
The image of A after a reflection using the y-axis.
The reflection of point (x, y) across the y-axis is (-x, y).
So, the image of point A is (-2, -1)
The image of A after a rotation of 180° using center (0, 0)
Rule: (x, y) becomes (-y, x)
So, the image of point A is (1, 2)
Therefore, the image of A after a reflection using the y-axis is (-2, -1).
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Look at recent question
Answer:
ok was it college math if so the I don't know
use ⧍ABC and assume B = 90°.
2. Findcgiven m∠A=57° and a=22
Answer:
1
Step-by-step explanation:
Answer: c = 14.287 approximately
==========================================================
Work Shown:
Refer to the diagram below. Note how side a is opposite angle A, and side c is opposite angle C.
tan(angle) = opposite/adjacent
tan(A) = a/c
tan(57) = 22/c
c*tan(57) = 22
c = 22/tan(57)
c = 14.2869670503452
c = 14.287
This value is approximate. Make sure your calculator is in degree mode
A rectangle is 13 feet long and 4 feet wide. Find its area.
Step-by-step explanation:
13 feet long
4 feet wide
13 + 4 = 17
feet long
feet wide
= feet wide
so 13 +14 = 17 feet wide
I need to know the answer
Answer: \(f(x)=-(x-5)^{2}(x+2)\)
Step-by-step explanation:
There is a double root at x=5 and a single root at x=-2, so we know f(x) is of the form \(f(x)=a(x-5)^{2}(x+2)\) for some constant a.
To find a, we can substitute the coordinates of the y-intercept, (0, -50).
\(-50=a(0-5)^{2}(0+2)\\\\-50=50a\\\\a=-1\)
So, \(f(x)=-(x-5)^{2}(x+2)\)
Gabrielle's age is two times Mikhail's age. The sum of their ages is 57. What is Mikhail's age?
Answer:
Mikhail's age is 19
Step-by-step explanation:
Divide 57 by 1/3. This is Mikhails age. This means that Gabrielle is 38. The sum of their ages is 57.
Answer:
19 years old
Step-by-step explanation:
Let x be Mikhail's age, then Gabrielle's age can be represented as 2x. We can use this information to set up an equation:
x+2x=57
Combine like terms
3x=57
Divide both sides by 3
x=19
19 years old
need some help on this problem
The equation is 3y / 3 = 2y / y. And the value of 'y' will be 2.
The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The equation is given as,
3y / 3 = 2y / y
Simplify the equation, then we have
3y / 3 = 2y / y
3y / 3 = 2
y = 2
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Find the area of the figure. (Sides meet at right angles.)
Answer:
70 in^2
Step-by-step explanation:
Make a line through the middle separating the 5 by 5 square and the rectangle. Then you find the individual areas of each. The bottom shape is a 5 by 5 square, so 5*5 is 25. The top shape's length is 5+2+2 because the bottom shape is a square, so each side=5. Then the blank space between both of the length 2's is 5. As a result, the rectangle's dimensions is 9 by 5. 9*5=45. When we add both areas, we get 45+25=70
Jessica and Emily went shopping at a local boutique. Jessica purchased 4 bracelets and a new.pair of earrings for $9.50. Emily purchased 3 new bracelets and 2 new pair of earrings for $10.25.
7 of 13-(18÷6+3)÷(9×3-25)
Answer:
3.
The moltiplications and divisions have priority over the sums and subtractions
Step-by-step explanation:
\( \:(3 + 3) \div (27 - 25)\)
\( \:(6 \div 2) = 3\)
g The probability of rolling a single die and obtaining a two is one-sixth. The probability of rolling a single die and obtaining a five is one-sixth. What is the probability of rolling a single die and obtaining either a two or a five
Answer:
33.33% or \(\frac{2}{6}\)
Step-by-step explanation:
A single die has a total of six different possible outcomes (1, 2, 3, 4, 5, 6). Since the numbers two and five are only two of the six possible outcomes that means that the possibility of getting one of these two numbers on a single roll is \(\frac{2}{6}\) . If we divide this fraction and multiply the result by 100 (0.333 * 100 = 33.33) we see that there is a 33.33% chance of you rolling either a two or a five.
Solve for the value of p.
(7p+7)°
33°
Answer:
p=20°
Step-by-step explanation:
(7p+7)°+33°=180°
7p°+7°+33°=180°
Step 1: Simplify both sides of the equation.
7p°+7°+33°=180°
(7p)°+(7+33)°=180°(Combine Like Terms)
7p°+40°=180°
7p°+40°=180°
Step 2: Subtract 40 from both sides.
7p°+40°−40°=180°−40°
7p°=140°
Step 3: Divide both sides by 7.
7p°/7°=140°/7°
p=20°
At the Dream Cone ice cream shop, there are
540 ways to make an ice cream sundae
consisting of one flavor of ice cream, one
topping, and one type of syrup. If there are 9
ice cream flavors and 5 types of syrup, how
many toppings are there?
Answer:
12 toppings
Step-by-step explanation:
5*9=45
540/45=12
The number of toppings in the ice cream cone are 9.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, there are 540 ways to make an ice cream sundae consisting of one flavor of ice cream, one topping, and one type of syrup.
Let the number of toppings be x.
So, 9×5×x=540
⇒ 45x=540
⇒ x=9
Therefore, the number of toppings in the ice cream cone are 9.
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One brand of cola co fizz is sold in packs of 4*500ml for 2.50 another brand colo is sold in packs of 10 330mlfo $2 which brand is more expensive
Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.
To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.
For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.
For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.
Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.
Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.
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Integrated Potato Chips paid a $2 per share dividend yesterday. You expect the dividend to grow steadily at a rate of 4 percent per year. a. What is the expected dividend in each of the next 3 years? b. If the discount rate for the stock is 12 percent, at what price will the stock sell? c. What is the expected stock price 3 years from now? d. If you buy the stock and plan to hold it for 3 years, what payments will you receive? What is the present value of those payments? Compare your answer to (b).
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
Dividend paid (D) = $2
Growth rate (g) = 4% per annum = 0.04
Expected Dividend in each of the next 3 years :
1st year : $2 * 1.04 = $2.08
2nd year : $2.08 * 1.04 = $2.16
3rd year: $2.16 * 1.04 = 2.2464 = $2.25
B) If the discount rate for the stock is 12 percent, at what price will the stock sell?
Discount rate (r) = 12% = 0.12
Price of stock = Dividend / (r - g)
Price of stock = 2 / (0.12 - 0.04)
Price = 2 / 0.08 = $25
c. What is the expected stock price 3 years from now?
(2.25 * 1.04) / 0.08
2.34 / 0.08 = $29.25
D) If you buy the stock and plan to hold it for 3 years, what payments will you receive? What is the present value of those payments?
Dividend to be received from year 1 to 3
2.08, 2.16, 2.25
Stock price in 3rd year = 29.25
Present value :
(29.25/1.12^3) + (2.25/1.12^3) + (2.16/1.12^2) + (2.08 / 1.12^1) = 26.00
For year 1 :
D = 2.08
Stock price = 2.16/0.08 = 27
Present value (PV) = (27/1.12) + (2.08/1.12) = 25.96
Year 2 :
D = 2.16
Stock price = 2.25/0.08 = 28.125
cashflow = (2.16 + 28.125) = 30.285
PV = (28.125/1.12^2) + (2.16/1.12^2) + (2.08/1.12^1) = 26.00
Year 3:
D = 2.25
STOCK PRICE = 29.25
Total Cashflow = (2.25 + 29.25) = 31.5
PV = (31.5/1.12^3) + (2.25/1.12^3) + (2.16/1.12^2) + (2.08/1.12^1) = $27.60
Which is greater? 2.17 or 2.2
Answer:
2.2 because the 2.2 can be 2.20
The number 2.2 is greater than 2.17.
To determine which number is greater between 2.17 and 2.2, we can compare the digits in each decimal number from left to right. Starting with the first decimal place, we compare the digits "1" and "2". Since 2 is greater than 1, we can conclude that 2.2 is greater than 2.17.
The decimal concept is a way of representing numbers that fall between whole numbers. It is based on the decimal system, which uses a base of 10. In the decimal system, a decimal point is used to separate the whole number part from the fractional part. The digits to the right of the decimal point represent fractions or parts of a whole. Decimals can also be expressed as percentages or fractions. For instance, 0.5 can be written as 50% or 1/2.
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Plssss help.........
It’s geometry.......
Answer: me to
Step-by-step explanation:
Answer: EGD
Step-by-step explanation:
Question Tell whether the statement is true or false. If A is 15% of B, then B:A is 85:15. Please Help!!!
Question
You wish to take out a $375,000 mortgage, which is to be paid monthly. The yearly interest rate on the loan is 3% and the
loan is for 25 years. Calculate the total interest paid over the life of the loan.
Round your answer to the nearest dollar.
Do NOT round until you have calculated the final answer.
Provide your answer below:
Answer:$158,488
Step-by-step explanation:
We have P0=$375,000,r=0.03,k=12,N=25, so substituting in the numbers into the formula gives
$375,000=d(1−(1+0.0312)−25⋅12)(0.0312),
that is,
$375,000=210.87645d⟹d=$1,778.2924.
To calculate the total interest, we have
$1,778.2924×25×12−$375,000=$158,488.
Answer: $1778.29
$375000 = 210.878645d > d = $1778.29
Solve for x: |2x + 6| − 4 = 20 Solve 2(x + 1) = 2x + 5.
Answer:
1. has two solutions x=9 and x=-15
2. 0=3 (no solution)
the equation p=52+0.04w models relation between the amount of water bill payment p in dollars and the number of units of water w in slope of equation
The slope in the equation p = 52 + 0.04w represents the rate of change in the water bill payment for each additional unit of water consumed.
Specifically, the slope of 0.04 indicates that for every increase of one unit in the number of water units (w), the water bill payment (p) will increase by 0.04 dollars.
This means that the slope represents the incremental cost of each additional unit of water.
In practical terms, the slope of 0.04 implies that for every additional unit of water consumed, the water bill will increase by $0.04.
This indicates a constant rate of increase in the water bill for each additional unit of water used.
It's important to note that the slope remains constant throughout the equation, suggesting a linear relationship between the amount of water consumed and the corresponding bill payment.
Therefore, The slope, in this case, is the coefficient of the variable w, which is 0.04.
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The probable question may be:
What is the meaning of the slope in the equation p = 52 + 0.04w, which models the relationship between the water bill payment p in dollars and the number of units of water w ?
Please help me! It isn’t hard im just not sure how to do it .
Answer:
a. Semester 1: 86.8, Semester 2: 87
b. Semester 1: 5.7, Semester 2: 6.3
c. Semester 1 because the standard deviation of the first semester was lower than of the second. This shows that his scores were closer to the mean and therefore he was more consistent.
Step-by-step explanation: Find the mean by taking the sum of the values for each semester and divide that sum by the number of values to find the average. Do this for both semesters. Now, find the absolute value of the difference between the mean and each value of the corresponding data set. Square each if those differences and sum them up. Now divide that sum by the number of data values and take the square root. This number is your standard deviation. You will use the standard deviations to make the comparison for part c. I hope this makes sense and helps!!!!
What variable do I solve for first? Do I solve for X because it’s first in the alphabet? If so, which X variable do I solve for? Do I solve for the smallest or biggest? I added a photo of the one i’m struggling with! :))
Answer:
No solution
Step-by-step explanation:
Given the simultaenous equations:
\(\displaystyle{\begin{cases} 3.25x - 1.5y = 1.25 \\ 13x-6y=10 \end{cases}}\)
The first equation can be rewritten as:
\(\displaystyle{\dfrac{325}{100} x - \dfrac{15}{10}y = \dfrac{125}{100}}\)
Clear the denominators by multiplying both sides with 100:
\(\displaystyle{\dfrac{325}{100} x \cdot 100 - \dfrac{15}{10}y \cdot 100= \dfrac{125}{100} \cdot 100}\\\\\displaystyle{325x - 150y = 125}\)
The whole terms are multiple of 25, so we can simplify even lower by dividing both sides by 25:
\(\displaystyle{\dfrac{325x}{25} - \dfrac{150y}{25} = \dfrac{125}{25}}\\\\\displaystyle{13x-6y=5}\)
So now, we have:
\(\displaystyle{\begin{cases}13x-6y=5\\ 13x-6y=10 \end{cases}}\)
There are various ways to solve simultaenous equations but I'll use the elimination method. Multiply negative in either first or second equation but I'll choose first:
\(\displaystyle{\begin{cases}-13x+6y=-5\\ 13x-6y=10 \end{cases}}\)
Add both equations with like terms:
\(\displaystyle{0=5}\)
Since this equation is false. Therefore, there is no solution to the simultaenous equation.
Answer:
first you look at what you have, then develop a strategythis system has No SolutionStep-by-step explanation:
You want to know what to do first with the system of equations ...
3.25x -1.5y = 1.2513x -6y = 10StrategiesYou are taught a couple of strategies for solving systems of linear equations algebraically. The "substitution" strategy requires you use one of the equations to write an expression that can be substituted into the other equation. The purpose of this is to reduce the number of variables in the remaining equation. Usually, that means solving for one of the variables to obtain the expression to substitute.
Another strategy you are taught is the "elimination" strategy. It is also called the "addition" or "combination" strategy. It is executed by adding (or subtracting) some multiple of one of the equations from the other equation, or some multiple of it. The purpose of this is to make the coefficient of one of the variables be zero in the combined equation.
LookSubstitutionThe substitution strategy is easiest to execute if you already have one or both equations in "y=" or "x=" form. It is nearly as easy to execute if the coefficient of one of the variables is +1 or -1, or if that can be easily made to be the case. So, this is what you look for to see if the substitution strategy is an appropriate choice.
EliminationThe elimination strategy is easiest to execute if the coefficients of one of the variables are the same or opposites. If they are the same, that variable can be eliminated by subtracting one equation from the other. If they are opposites, the variable can be eliminated by adding one equation to the other. So, this relation between coefficients is one of the next things you look for when deciding what your strategy will be.
The elimination strategy can also be effectively used if the coefficients of one of the variables are a nice (integer) multiple of one another. In this problem, we notice that the coefficients of y are -1.5 and -6, which are related by a factor of 4. (It is helpful to be very familiar with multiplication facts.) As it happens, the coefficients of x have the same relation: 13 is 4 times 3.25.
Dependent/InconsistentThe fact that both sets of coefficients are related by the same factor raises a red flag regarding these equations. It means they are either dependent (have infinite solutions) or are inconsistent (have no solution).
The equations are dependent if one equation is a multiple of the other. Here, we can check that by multiplying the first equation by 4:
4 × (3.25x -1.5y) = 4 × 1.25
13x -6y = 5
We notice the other equation is ...
13x -6y = 10
Values of x and y that make 13x-6y=5 cannot also make that same sum be 10. These are called "inconsistent" equations, and they have No Solution.
Hypothetical: If the first equation were 3.25x -1.5y = 2.5, then multiplying it by 4 would give 13x -6y = 10, the same as the second equation. In this case, the equations would be called "dependent," and any of the infinite number of solutions to the first equation would also be a solution to the second equation.
PlanAfter you look at the equations to determine if any of the coefficients are 1, or have nice relations with the coefficients of the other equation, you can formulate a strategy for elimination or substitution. As we saw above, it can be useful to eliminate any fractions to start with. Sometimes, it is also useful to factor out any common factors. For example, 2x + 6y = 8 can be reduced to x +3y = 4 by factoring out 2 from every term.
Then, the variable that you solve for first will be the one that is left after you have done your substitution or elimination.
This SystemAs we saw above, the given equations can be rewritten as ...
13x -6y = 5 . . . . . . first equation multiplied by 413x -6y = 10We already know the same coefficients and different constants mean these equations are inconsistent and have No Solution. If we need further convincing we can subtract one from the other. Here, too, we can plan ahead a little bit: subtracting the first from the second will leave a positive constant:
(13x -6y) -(13x -6y) = (10) -(5)
0 = 5 . . . . . . . simplify (false)
There are no values of x and y that will make this false statement true, hence no solution.
jalen drew a rectangle with a perimeter of 20 inches. the smaller side measured 3 inches. jalen said the longer side of the rectangle had to be 7 inches. is jalen correct?
Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);
P = 2(L + W)
Where:
P represent the perimeter of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;
P = 2(3 + 7)
20 = 2(10)
20 = 20 (True).
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what is a logarithm?
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x,
So in other words, a logarithm is the power to which a number must be raised in order to get some other number . For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. because. 102 = 100.
Hope this helps. Have a good day!