Answer:
38
Step-by-step explanation:
Using the volume of the cylinder and the prism, find the volume of the composite shape. Remember, the prism has been removed from the cylinder.
Diameter of cylinder base - 19.8
base area of cylinder - 307.8
volume of cylinder - 9.234
base area of the prism - 196
volume of the prism - 6.186
When the prism is taken out of the cylinder, the composite shape's volume is 3.048.
what is volume ?The volume of an item in three dimensions is the area that is enclosed by its boundaries. The space that an object occupies in three dimensions is measured by its volume, which is given in cubic units. A few of illustrations of cubic units are cm3 and in3. On the other side, an item's mass is used to measure how much matter it contains. One typical method to ascertain an object's mass is to weigh it, either in pounds or kilogrammes. Unlike the primary equation for the square of a rectangular box, which would be length, breadth, and height, the primary equation in capacity is length, width, and height.
given
volume of cylinder - 9.234
volume of the prism - 6.186
the volume of composite shape is = volume of cylinder - volume of prism
= 9.234 - 6.186
= 3.048
When the prism is taken out of the cylinder, the composite shape's volume is 3.048.
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Convert the decimal
0.9
2
¯
to a fraction.
Read the following prompt and type your response in the space provided.
Describe a real-life representation of the following.
12/49=0.24
A real - life representation of 12 / 49 = 0. 24 is the cost of a single donut in a 49 pack of donuts that cost $ 12.00
What real - life representation shows the equation ?The equation is 12 / 49 = 0. 24. A real - life representation of this could have to do with unit cost, and total cost.
The 12 could be the total cost of a package of donuts that have 49 donuts inside.
The unit cost of each of these donuts would therefore be:
= Total cost of donuts / Number of donuts in package
= 12 / 49
= $ 0.24 per donut
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suppose that you have a photograph and you want to crop it to cut off 2 inches from the right side of the picture and then resize it using various scale factors (for our purposes here we will focus on a scale factor of 1.5). the transition from the dimensions of the original photograph to the dimensions of any scaled version is a two-step process.
Yes, cropping a picture and then using a scale factor to resize it is a two-step process.
The image is first cropped by subtracting 2 inches from the right side, altering the image's proportions.
The image is then enlarged using a scale factor of 1.5, which increases the image's dimensions by 1.5.
The final measurements of the image would be its original measurements less 2 inches (for cropping), then multiplied by 1.5. (for the resizing).
It's vital to keep in mind that both picture cropping and image scaling change the size of the final product.
Yes, cropping a photo, then resizing it with a scale factor, is a two-step process.
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What is the area, in square meters, of the shaded part of the rectangle below? 9 m 20 m 4 m
49 is the shaded part of the rectangle.
What are the names of the shaded areas?Therefore, the rule for its area is base1+base2/2xh
Base1=9
Base2=20
Height = 4
Therefore, 9+20/2 x 4= 49.
The denominator is the total number of pieces that make up the whole, which is eight. That is the figure beneath the fraction bar. The numerator is the number of shaded portions, which is 7. That is the value shown above the fraction bar.
The shaded region’s area is the difference between the area of the complete polygon and the area of the polygon’s unshaded portion. In polygons, the area of the shaded component can arise in two ways. The darkened zone might be found in the middle of a polygon or on its sides.
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The area of the shaded region of the rectangle is 130 sq. meter
What is Rectangle ?A quadrilateral with four right angles is a rectangle. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.
The denominator is the total number of pieces that make up the whole, which is eight. That is the figure beneath the fraction bar. The numerator is the number of shaded portions, which is 7. That is the value shown above the fraction bar.
The shaded region’s area is the difference between the area of the complete polygon and the area of the polygon’s unshaded portion. In polygons, the area of the shaded component can arise in two ways. The darkened zone might be found in the middle of a polygon or on its sides.
The base length = 9 m
The base width = 20 m
The height = 4m
The area of the shaded region = 1/2 *(9 + 4)*20 = 130 sq. meter
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What is the remainder of the quantity 2 x squared plus 7 x minus 39 end quantity divided by the quantity x minus 7 end quantity? Please show all work
The remainder of the division is (x-3)(x+13)/x-7
How to determine the reminderFrom the information given, we have that;
2 x squared plus 7 x minus 39 end quantity quantity x minus 7 end quantityThis is represented as;
2x² + 7x - 39/x - 7
Now, factorize the numerator
Find the pair factors of -78 that sum up to 7, then substitute the value, we have;
2x² + 13x - 6x - 39/x- 7
(2x² + 13x) - (6x-39)/x-7
Factor the common terms
x(x + 13) - 3(x + 13)/x-7
Then, we get;
(x-3)(x+13)/x-7
Hence, the value is (x-3)(x+13)/x-7
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Which expression is equivalent to 5f+4f?
Hey there!
Answer:
An equivalent to the given expression [tex]5f+4f[/tex] would be [tex]9f[/tex].
Hope this helps!
Answer:I hope this helps
Step-by-step explanation:
5f+4f
Collect like terms by adding their coefficients
which is like this
(5f+4f)f and now we
Add the numbers in the parentheses
=9f
In circle O O, O P = 2 OP=2 and the length of ⌢ = 7 9 π PQ ⌢ = 9 7 π. Find the area shaded below. Express your answer as a fraction times π π.
The measure of angle POQ is given as follows:
30º.
What is the area of a circle?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr²
The radius of the circle in this problem is given as follows:
r = OP = 2.
(distance of the center O to point P on the circumference).
Hence the area of the circle is given as follows:
A = 4π.
The area of the sector is given as follows:
π/3.
The ratio of the area of the sector and the area of the circumference is given as follows:
(π/3)/(4π) = 1/12.
The entire area has a measure of 360º, hence the angle measure is obtained as follows:
1/12 x 360 = 30º.
Missing InformationThe problem is given by the image presented at the end of the answer.
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While playing a board game, Vy noticed that the die landed on the number 1 more often than usual.
Part A: Describe a simulation that could be run to test how many times out of 100 a fair die should land on the number 1. State the representations and possible outcomes. Be sure to give enough detail that another person could replicate your simulation. (7 points)
Part B: While running a simulation, the die landed on the number 1 a total of 26 times out of the 100 rolls. Construct and interpret a 95% confidence interval for the true proportion of rolls that will land on the number 5. Show all work. (7 points)
Part C: Does the confidence interval in part B support Vy's suspicions that the die is not fair? Explain your reasoning. (6 points)
a) A procedure that could be run to test how many times out of 100 a fair die should land on the number 1 is given as follows: Select a random number out of six 100 times, with 1 constituting a success and the remaining five numbers constituting a failure.
b) The 95% confidence interval for the true proportion of rolls that will land on the number 1 is given as follows: (0.174, 0.346). The interpretation is that we are 95% sure that the proportion of all rolls that land in one is between these two values.
c) As the lower bound of the interval is above the expected proportion of 0.1667, the confidence interval supports Vy's suspicions that the die is not fair.
How to design the procedure?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
A die has six sides, one out of which is one, hence the probability of a one being rolled is given as follows:
p = 1/6 = 0.1667.
Hence 100 trials of a procedure with 6 results should be used, in which:
One result represents a success.The remaining five results represent failure.What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for this problem are given as follows:
[tex]n = 100, \pi = \frac{26}{100} = 0.26[/tex]
Then the lower bound of the interval is calculated as follows:
[tex]0.26 - 1.96\sqrt{\frac{0.26(0.74)}{100}} = 0.174[/tex]
The upper bound is calculated as follows:
[tex]0.26 + 1.96\sqrt{\frac{0.26(0.74)}{100}} = 0.346[/tex]
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Joseph buys 11 bottles of apple juice at the corner store for a total cost of $9.68. If
each bottle costs the same amount, how much is 12 bottles of juice?
Answer: $
Submit Answer
Answer:
10.56
Step-by-step explanation:
A coin is flipped 200 times. The table shows the frequency of each event.
Outcome Frequency
Heads 96
Tails 104
Determine the experimental probability of landing on tails.
50%
52%
96%
104%
Answer:
52%
Step-by-step explanation:
Since the question asks about tails, we don't need the information about heads.
So out of 200 flips, 104 were tails. If we put 104 out of 200 in fraction form, you get;
104
-----
200
Now we just divide;
104/200 = 0.52, also known as 52%
Find the average rate of change of the function on the interval specified for real number b.
f(x) = 4x2 − 7 on [1, b]
The average rate of change on the interval [1, b] is:
r = 4*(b + 1)
How to find the average rate of change?For a function f(x), we define the average rate of change on the interval [a, b] as:
r = ( f(b) - f(a))/(b - a)
Here we have the function:
f(x) = 4x² - 7
And the interval is [1, b]
Then the average rate of change is:
r = (f(b) - f(1))/(b - 1)
r = ( 4b² - 7 - 4 + 7)/(b - 1)
r = (4b² - 4)/(b - 1)
r = 4*(b² - 1)/(b - 1)
r = 4*(b + 1)*(b - 1)/(b - 1)
r = 4*(b + 1)
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The venn diagram shows sports played by 10 students let event A= The student play basketball let event B= the student plays soccer
The value of P(A|B) from the given data is 1/6 ≅ 0.17
Conditional Probability:The term P(A/B) is known as a conditional probability which indicates the probability of an event A that depends on another event B.
The probability of an event or outcome occurring due to the existence of a prior event or outcome is known as conditional probability.
P(A/B) is used to find this conditional probability.
The formula for P(A/B) is given by
P(B/A) = P(A∩B) / P(A)Here we have
A ven diagram which shows sports played by 10 students
From given figure
Number of students who play basketball, p(A) = 3
Number of students who play soccer, p(B) = 2
Number of students who play both games, A∩B = 3
As we know, P(A/B) = P(A∩B)/P(B)
= 1/3 [2]
= 1/6 ≅ 0.17
Therefore,
The value of P(A/B) from the given data is 1/6 ≅ 0.17
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Modeling Problems with Equations Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run? A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by. Select all that apply. You know the difference in the distances the boys ran, so this is a subtraction problem. You are finding the total distance the boys ran, so this is an addition problem. Dean ran part of the distance Sam ran, so this is a multiplication problem. The correct equation is s + 2.3 = 6.8. The correct equation is s – 2.3 = 6.8. The correct equation is 2.3s = 6.8.
Since Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, the true statements about the distance which Sam ran are:
A. You know the difference in the distances the boys ran, so this is a subtraction problem.
E. The correct equation is s – 2.3 = 6.8.
What is distance?In Mathematics, distance can be defined as the total amount of ground that is covered or travelled by a physical object (body) over a particular period of time and speed, irrespective of its direction, starting point or ending point.
Since Dean ran 6.8 km and 2.3 fewer kilometers than Sam, we can logically deduce that this is a subtraction problem. Assuming the variable s represent the distance which Sam ran, Sam's distance can be calculated as follows;
s – 2.3 = 6.8
s = 6.8 + 2.3
s = 9.1 kilometers.
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write an equation of the line that passes through (-6,0) and (0,-24)
Answer:
y=-4x-24
Step-by-step explanation:
draw the line on a grid paper so that you know the slope must be negative. then plug in the numbers.
the solid with a semicicular base of radius 5 whose cross sections perpendicular to the base and parallel to the diameter are squares
The volume of the solid with the given semi-circular base with radius 5 units is equal to 333.33 cubic units.
As given in the question,
Radius of the semicircular base = 5 units
Equation of the circle is given by :
x² + y² = r²
⇒ x² + y² = 5²
⇒ x² + y² = 25
⇒ x = √25 - y²
Cross section is perpendicular to the base and it is parallel to the diameter are squares:
Diameter is double of the radius
s = 2x
= 2√25 - y²
Volume of the given solid is equal to :
V = [tex]\int\limits^5_0 {s^{2} } \, dy[/tex]
= [tex]\int\limits^5_0 {( 2\sqrt{25 - y^{2} }) ^{2} } \, dy[/tex]
= [tex]\int\limits^5_0 {( 4({25 - y^{2} }) } \, dy[/tex]
= 100y - 4y³/3 (for limit 0 to 5)
= ( 500 - 500/3 ) - 0
= 500 ( 1 - 1/3 )
= 500( 2/3 )
= 1,000/3
= 333.33 cubic units.
Therefore, the volume of the given solid with the given measures is equal to 333.33.
The above question is incomplete, the complete question is :
Use the general slicing method to find the volume of the following solid.
The solid with a semicircular base of radius 5 whose cross sections perpendicular to the base and parallel to the diameter are squares. Place the semicircle on the xy-plane so that its diameter is on the x-axis and it is centered on the y-axis. Set up the integral that gives the volume of the solid. Use increasing limits of integration.
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At Lauren's school library, students are allowed to have a balance of no less than -$12 and still check out books. Five days ago, Lauren's balance was $0, but now she owes for her books that are five days late. If the total charge on her checked out books is $2 per day and she turns them in today, can she still check out books? No Yes
Answer:
No
Step-by-step explanation:
2 * 5 = 10
12 does not equal 10
Let f(x) = 2√x.
If g(x) is the graph of f(x) shifted down 1 units and right 6 units, write a formula for g(x).
The formula for g(x) is 2√(x-6) + 1. The solution has been obtained using the concept of translation.
What is translation?
In mathematics, a translation involves moving a shape up, down, left, or right. The translated shapes appear to be exactly the same size as the original ones; thus, the shapes are consistent with one another. Just one or more directions have been changed. There is no change to the shape because it is simply being moved from one location to another.
The object's shift in location can occur in a variety of ways, such as initially moving left, then turning right, and so on. Each point on the form will translate by the same number of units.
We are given f(x) = 2√x
Now, shifted down 1 unit, we get
2√x + 1
Also, shifted right 6 units, we get
2√(x-6)
So, g(x) = 2√(x-6) + 1
Hence, the formula for g(x) is 2√(x-6) + 1.
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Select the correct answer.
Which expression is equivalent to the given expression? Assume the denominator does not equal zero. a^3b^35/a^4b
By Assuming the denominator does not equal zero. a³b³/a⁴b equivalent expression is b⁴/a.
What is an equivalent expression?
Equivalent expressions are expressions that have the same result when they are simplified.
Two expressions are considered equivalent if they can be transformed into each other by applying mathematical operations such as simplification, combining like terms, or applying the properties of arithmetic and algebra.
Equivalent expressions can be used to solve problems more efficiently or to help understand complex mathematical concepts.
For example, simplifying an expression to its simplest form can make it easier to understand or perform further calculations with it.
Equivalent expressions can also be used to check the correctness of a solution to a problem, by verifying that the answer can be transformed into the expected result.
The given expression can be simplified as follows:
a³b³ / a⁴b = (a³/a⁴) * (b³/b)
a³/a⁴ = 1/a
b³/b = b²
Hence, By Assuming the denominator does not equal zero. a³b³/a⁴b equivalent expression is b⁴/a.
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Please help me I need this.
Answer:
y= - 2,0
x=0,-5
slope would be y=MX+Y
so -2= -5(0)+0
1) Identify the quadrant in which the point belongs. (-17,-87)
The point (-17, -87) belongs to the third quadrant
How to determine the quadrant of the pointFrom the question, we have the following parameters that can be used in our computation:
Point = (-17, -87)
In the above point, we have
x = -17 and y = -87
This means that the x and the y coordinates are negative
The quadrant where the x and the y coordinates are negative is the third quadrant
Hence, the point is in the third quadrant
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TRUE OR FALSE deciding that a process that fills bottles with soda is functioning properly by checking the weights for a sample of bottles is an example of inferential statistics.
True, Deciding that a process that fills bottles with soda is functioning properly by checking the weights for a sample of bottles is an example of inferential statistics.
A subset of statistics known as inferential statistics uses a variety of analytical techniques to extrapolate conclusions about population data from sample data.
It is an example of inferential statistics because you are using a sample of data to make inferences about the population of bottles being filled, rather than measuring the weight of every bottle.
Hence, Deciding that a process that fills bottles with soda is functioning properly by checking the weights for a sample of bottles is an example of inferential statistics.
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I'm not sure how to answer part b, an explanation would be appreciated.
The true statement is that the sample mean is not biased
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Sample selection of 2
The sample is selected such that all 4 samples are equally likely
This means that
P(Each selection) = 1/4
An unbiased sample is such that reflects all members of the population and in this case, this sample reflects the population
Hence, the sample is unbiased
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factor $(x^2 y^2-z^2)^2-4x^2y^2$ as the product of four polynomials of degree $1$, each of which has a positive coefficient of $x$. all coefficients appearing in your factorization should be integers. within each factor, arrange the terms so that variables appear in alphabetic order and the constant term, if any, is at the end. (this will help ensure accurate grading.)
We can factor [tex]$(x^2 y^2-z^2)^2-4x^2y^2$[/tex]as:
[tex]$(x^2 y^2-z^2)^2-4x^2y^2 = (x^2 y^2-z^2-2xy\sqrt{2})(x^2 y^2-z^2+2xy\sqrt{2})$[/tex]
To calculate this:
We can see that each factor is of degree 1 and has a positive coefficient of x.
In each factor, the variables appear in alphabetic order, with the constant term at the end.
In order to factor this expression, we first use the difference of squares, by breaking it down [tex]$(x^2 y^2-z^2)^2$[/tex] as [tex]$(x^2 y^2-z^2)(x^2 y^2-z^2)$[/tex]
We can then add and subtract a suitable term, here we added and subtract 2xy * √2, to make one of the terms in each of the brackets match one of the terms of the original expression, so we can factor it out.
So, [tex]$(x^2 y^2-z^2)^2-4x^2y^2 = (x^2 y^2-z^2-2xy\sqrt{2})(x^2 y^2-z^2+2xy\sqrt{2})$[/tex].
Factors are the numbers that divide into a given number without leaving a remainder.
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Left F(x) be the number, in thousands, of vehicles a manufacturer estimates will be sold when x million dollars are spent on advertising. If f(1.8)=240, and f(2.5)=325, compute the average rate of change for 1.8 < x< 2.5
The average rate of change for 1.8 < x < 2.5 is given as follows:
121.43.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output divided by the change in the input.
The change in the output for this problem is given as follows:
325 - 240 = 85.
The change in the input for this problem is given as follows:
2.5 - 1.8 = 0.7.
Hence the average rate of change is given as follows:
85/0.7 = 121.43.
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Sam has 9 1/3 cups of cereal. Each serving is 2/4 cup. How many servings does Sam have?
The number of servings that Sam has would be = 18.67 servings.
What is a fraction?A fraction is part of a whole value that is being represented in a form of numerator and denominator.
The number of cups that Sam has = 9 1/3 = 28/3
The number of cups used for each serving = 2/4
That is ;
1 serving = 2/4 cups
X servings = 28/3 cups
Make X the subject of formula;
X servings = 28/3 ÷ 2/4
= 28/3 × 4/2
= 112/ 6
= 18.67 servings.
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which of the following expressions have dimensions of length? assume the standard variables have the following dimensions: t is in units of s, x is in units of m, v is in units of m/s, and a is in units of m/s2.a. atb. 1/2at^2c. x^3/td. √2axe. v^2/a
The following expressions have length dimensions: a. at b. x3/t
d. √2ax
a. at: has a dimension of m because it is the product of acceleration (m/s2) and time(s). b. 1/2at2: has a dimension of m because it is the product of acceleration (m/s2) and time(s) squared. c. x3/t: has a dimension of m because it is the product of distance x (m) cubed and time(s).
e. v2/a: is a product of velocity (m/s) squared and acceleration (m/s2) thus it doesn't have a dimension of length. d. 2ax: is a product of 2, distance x (m), and acceleration (m/s2) so it has dimension of m.
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42. HOW DO YOU SEE IT?
Write an expression in rational
exponent form that represents
the side length of the square.
Area:
x in.²
The expression for the side of the square will be s=x^(1/2) in
where s=side.
what are squares?
A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.
The most important properties of a square are listed below:
All four interior angles are equal to 90°.All four sides of the square are congruent or equal to each other.The opposite sides of the square are parallel to each other.The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other.The square has 4 vertices and 4 sides.The diagonal of the square divides into two similar isosceles triangles.The length of diagonals is greater than the sides of the square.Area of square=(side)²
Perimeter of square=4*side
Now,
Area of square=(side)²
and given that
A=x in^2
s^2=x
s=√x
Therefore, expression in rational exponent form will be
s=x^(1/2)
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Please answer this question
Answer:
Step-by-step explanation:
7x9=63
because 7 down times 9 across
The path of a firework can be represented by F9t=16^+92t+160
What is the maximum height of the firework?
How long did it take to reach its maximum height?
a) The maximum height of a firework is 292.25 feet.
b) The time required by a firework to reach its maximum height is 2.875 second.
How to determine the maximum height reached by a firework and its time needed
Herein we find the case of a firework being launched under free fall motion, that is, a vertical uniformly accelerated motion due to gravity, represented by following quadratic equation:
f(t) = - 16 · t² + 92 · t + 160
Where:
f(t) - Height, in feett - Time, in secondsPart A - The maximum height can be found by modifying the quadratic equation into vertex form. This can be done by completing the square:
f(t) = - 16 · t² + 92 · t + 160
f(t) = - 16 · [t² - (23 / 4) · t - 10]
f(t) - 16 · (529 / 64) = - 16 · [t² - (23 / 4) · t + 529 / 64] + 160
f(t) - 292.25 = 16 · (t - 2.875)²
The firework reaches a maximum height of 292.25 feet.
Part B - The firework takes a time of 2.875 seconds to reach its maximum height.
RemarkFree fall equation has several mistakes and was corrected according to principles of free fall motion.
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