Explain why the volume of these two stacks of quarters are equal? Use Cavaliens principle in your explanation (If you need to)
Answers
Given the word problem, we can deduce the following information:
1. Two stacks of 18 pennies each are shown.
To determine if the volumes of the given stacks of quarters are equal, we note that Cavelieri's Principle states:
The volumes of two solids are equal if the areas of the corresponding sections drawn parallel to some given plane are equal.
Since each penny in both stacks has the same base area and has the same number of pennies. Therefore, the volumes of the given stacks are equal.
Related Questions
A physician borrowed $100,000 from credit union for 9 months at annual interest rate of 4%. What is the simple interest due on the loan?
Answers
Givens.
• The amount borrowed was $100,000.
,• The time elapsed is 9 months.
,• The annual interest rate of 4%.
The simple interest formula is
[tex]I=PRT[/tex]Where P = 100,000, R = 0.04, and T = 9/12.
[tex]\begin{gathered} I=100,000\cdot0.04\cdot\frac{9}{12} \\ I=3,000 \end{gathered}[/tex]Therefore, the simple interest is $3,000.the answer would be 3,000
The graph of y=-2is is transformed to becomey=+5. Which of the folloA The graph is translated Sunits left and 2 units up.& The graph is translated 2 units left and Sunits ups.Oc.thegraph is mamiandumits left and sumits chosam.OD The graph is translated Sunits right and 2 units dow
Answers
Given the following function:
[tex]y=\sqrt{x-2}[/tex]notice that the transformation:
[tex]y=\sqrt{x}+5[/tex]can be written like this:
[tex]y=\sqrt{(x+2)-2}+5[/tex]first, the +2 means that the graph moves 2 units left, and the +5 makes the graph move 5 units up.
in one year, a town recorded a total of 79 days it did not rain, how many days did it rain
Answers
Answer:
286
Step-by-step explanation:
there are 365 in a year
365-79
286
if a || b, m<2=63°, and m<9=105°, find the missing measure of m<7=?
Answers
Vetical angles are on opposite sides of the intersection of two lines, in this case, when lines c and b intersect, <7 and <9 are formed, these angles are vertical and m<7 = m<9, then:
m<7 = 105°
Number of Inches in a Mile An inch is approximately1.57828 x 10-5 mile. Find the reciprocal of this num-ber to determine the number of inches in a mile.
Answers
We are given that an inch is approximately 1.57828x10⁻⁵ mile.
[tex]1\: inch=1.57828\times10^{-5}\: \text{mile}[/tex]The reciprocal of this number will give us the number of inches in a mile.
[tex]\frac{1}{1.57828\times10^{-5}\: }=63360\: inches[/tex]Therefore, a mile is approximately 63360 inches.
[tex]1\: mile=63360\: \text{inches}[/tex]INVERSES OF AN EXPONENTIAL FUNCTION 6). Fill in the chart. If needed, use a calculator and round to one decimal place.
Answers
We will have the following:
x f(x) = 4^x function(x,f(x)) inverse(f(x),x)
0 1 (0, 1) (1, 0)
1 4 (1, 4) (4, 0)
-1 1/4 (-1, 1/4) (1/4, -1)
2 16 (2, 16) (16, 2)
-2 1/16 (-2, 1/16) (1/16, -2)
Answer:
columns in order of 0/1/-1/2/-2
Step-by-step explanation:
g, h and s
e, a and b
d, q and r
k, f and c
m, l and n
True or false?
A "natural monopoly" is a market that runs very inefficiently when one large firm provides all of the output.
Answers
The following statement: A "natural monopoly" is a market that runs very inefficiently when one large firm provides all of the output is false.
A natural monopoly is a sort of monopoly that emerges because of the high start-up costs or substantial economies of scale associated with conducting business in a certain industry, which can result in large barriers to entry for potential rivals.
Natural monopolies can form in sectors that require specialized raw resources, technology, or other variables to function. Natural monopolies can also occur when one business is far more efficient than several enterprises in providing the market with the item or service.
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determine which of the following relations is a function.Xyxy-1010-32-55-1100025-5110-104O3-8-2124y-4-22346XOx01225y24267
Answers
The relation between the function is X cannot repeat itself.
We have given that,
functions table
We have to determine which relation is a function.
What is the function?
A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
The relation between the function is
X cannot repeat itself
Therefore option C is correct.
Complete question: Determine which of the following relations is a function [see in attachment]
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Your account number is 421746. You wish to deposit 120 dimes, 25 quarters, and checks for $184.63 and $196.17. You wish to receive $50.00 in cash. Complete the savings deposit slip.
Answers
The deposit slip would look like this:
we have that the currency is 120 dimes = $1.2 and 25 quarters = $6.25.
I need help with a table to plot the points
Answers
In order to plot a set of coordinates on a graph page, you would need to take account of every pair of x and y values provided. The line that goes horizontally is the x-axis (from left to right). All the negative values move from point zero (the origin).
The ordered pair, or the coordinates tells you where x and y intersect. For example, the first set of coordinates are (2, 9). That means, when x is 2, then y is 9.
Observe that x equals 2 on the right side of the horizontal axis. Next, you look for the spot where y equals 9.
Next step, you carefully trace the spot where x is 2, and trace it up a straight line and at the point where y equals 9 (at the upper part of the y axis), you put a tiny "X" to mark the spot where both values intersect.
Notice that while tracing from x, you move upwards, and while tracing from y, you move towards the right. That point defines the coordinates (2, 9) which is the first line on your table.
You follow a similar step for every one of the other coordinates, which are;
[tex]\begin{gathered} (2,9) \\ (4,3) \\ (6,-6) \\ (0,15) \\ (3,6) \\ (5,0) \\ (\frac{7}{3},8) \end{gathered}[/tex]Please note that I've just attached the same graph, but this time I've labelled the points one by one.
This should help with reading the coordinates at every point.
Hi! I need some help with my precalculus homework question, please. Thank you for your time.
Answers
If the point (4, -1) is a point on the graph of f, then f(4) = -1
First blank = 4
second blank = -1
Explanation:The given point: (4, -1)
From the point: the coordinate tells us x = 4, y = -1
For a graph of function f, f(x) is the same as y
To represent the point (4, -1) as a funtion of x (that is f(x)), we will replace x in f(x) with the value of the x coordinate. The result when we replace it will the value of the y coordinate
when x = 4
f(4) = the value of the y coordinate
f(4) = -1
To complete the blanks:
If the point (4, -1) is a point on the graph of f, then f(4) = -1
First blank = 4
second blank = -1
HELP NEEDED ASAP PLS
Answers
The expression in the simplest form is -9x/10 + (5).
What is termed as the simplification?Simplify simply means making something easier to understand. Simply or simplification in mathematics refers to reducing an expression / fraction / problem to a simpler form. It simplifies the problem by calculating and solving it.
We can —
Simplify fractions by removing all common factors from the numerator and denominator as well as composing the fraction in its simplest form.By grouping as well as combining similar terms, you can simplify mathematical expressions. This makes this same expression simple to understand and solve.For the given equation;
= (-3x/5 - 7) - (-12 + 3x/10)
open the parenthesis;
= -3x/5 - 7 + 12 - 3x/10
Bring the variable part together.
= -3x/5 - 3x/10 - 7 + 12
Add variables and constant separately.
= -9x/10 + 5
Thus, the simplest form of the given expression is found as -9x/10 + 5.
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If measure of angle 3 = (5x + 12)° and measure of angle 7 = (8x)° find the value of ‘x’.
Answers
The value of x is 21
The other angles are 63°, 117°, 63°, 117°
Given:
The angles of a parallelogram ABCD are
∠A = 3x°
∠B = (5x+12)°
To find:
The value of x
Parallelogram ABCD,
∠A and ∠B are two adjacent sides
Properties of a parallelograms
Two opposite sides are parallelogram are equal and parallel to each other.
So, the adjacent sides are supplementary angles i.e. sum is 180°.
The opposite angles are equal.
Now,
∠A + ∠B = 180°
⇒ 3x + (5x + 12) = 180
⇒ 3x + 5x + 12 = 180
⇒ 8x + 12 = 180
⇒ 8x = 180 - 12
⇒ 8x = 168
⇒ x = 168 ÷ 8
⇒ x = 21
Thus,
The value of x = 21
The angles are
∠A = 3x = 3 * 21 = 63°
∠B = (5x + 12) = (5 * 21 + 12) = 105 + 12 = 117°
As opposite angles are equal so
∠A = ∠C = 63°
∠B = ∠D = 117°
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RANGE AND DOMAIN. GRAPSWhat is the Range of this Relation:{(3,0), (-2,6), (-1,4), (-2,0), (1,5)}
Answers
Given the relation:
[tex]\mleft\{\mleft(3,0\mright),(-2,6),(-1,4),(-2,0),(1,5)\mright\}[/tex]The range of the relation can be thought of as the set of y-coordinates of a point (x, y). That is, as every second number of the ordered pairs. Additionally, the set should be ordered, and should not contain repeated values. This set is:
[tex]Range=\mleft\lbrace0,4,5,6\mright\rbrace[/tex]Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 61 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 8.3 and a standard deviation of 2.4. What is the 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
Answers
The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is 7.9067<m<8.6933.
What is a confidence interval?
In statistics, a confidence interval describes the likelihood that a sample size would fall between such a set range of values for a specific percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% likelihood that the true value comes inside that range if the following are examples of 10.00 produced using a statistical model with a 95% standard error of 9.50 - 10.50.In the study of chocolate chips,
sample size, n=61
mean, x=8.3
standard deviation, s=2.4
90% of the confidence interval
[tex]8.3-(\frac{1.28*2.4}{\sqrt{61} } ) < m < 8.3+(\frac{1.28*2.4}{\sqrt{61} } )[/tex]
7.9067<m<8.6933
The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is 7.9067<m<8.6933.
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Compare -2/3 to 3/4 is it equal, less.or greater
Answers
And
3/4 = 0.75
I suppose 3/4 is greater.
Answer:
less
Step-by-step explanation:
negative numbers are less than positive numbers
[tex]-\frac{2}{3} < \frac{3}{4}[/tex]
Hope this helps
if Robbie can do 35 Jumping Jacks in 60 seconds how many seconds would it take him to do 14 jumping jacks
Answers
Based on the number of jumping jacks that Robbie can do in 60 seconds, the number of seconds it will take to do 14 jumping jacks is 24 seconds
How to find the number of seconds?To find the number of seconds that it takes Robbie to do 14 jumping jacks, find the number of seconds it takes to do a single jumping jack.
The number of seconds to do a single jumping jack is:
= 60 / 35
= 1.71 seconds
If 14 jumping jacks are to be done then the number of seconds would be:
= 1.71 x 14
= 24 seconds
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determine if f, g, and h are true or false. If false, correct the statement with an explanation
Answers
We need to determine if the statements are true or false.
In order to do so, we need to pay attention to the following notations:
[tex]\begin{gathered} (\sin x)^{-1}=\frac{1}{\sin x} \\ \\ \sin^{-1}x=\text{ inverse function of }\sin x \end{gathered}[/tex]The same notations apply to cosine and tangent functions.
The inverse f⁻¹(x) is the function such that:
[tex](f^{-1}\circ f)(x)=f^{-1}(f(x))=x[/tex]Thus, we have:
[tex]\cos^{-1}(\cos(\frac{15\pi}{6}))=\frac{15\pi}{6}[/tex]Therefore, statement g. is true.
In order to show that statements f. and h. are false, let's see what happens for x = 1/2:
[tex]\begin{gathered} \frac{\sin^{-1}(\frac{1}{2})}{\cos^{-1}(\frac{1}{2})}=\frac{\frac{\pi}{6}}{\frac{\pi}{3}}=\frac{3}{6}=0.5\text{ \lparen no units\rparen} \\ \\ \tan^{-1}(\frac{1}{2})\cong0.46\text{ \lparen rad\rparen} \\ \\ \Rightarrow\frac{\sin^{-1}(\frac{1}{2})}{\cos^{-1}(\frac{1}{2})}\ne\tan^{-1}(\frac{1}{2}) \end{gathered}[/tex][tex]\begin{gathered} \sin^{-1}(\frac{1}{2})=\frac{\pi}{6}\cong0.52 \\ \\ \frac{1}{\sin(\frac{1}{2})}\cong2.09 \\ \\ \Rightarrow\sin^{-1}(\frac{1}{2})\ne\frac{1}{\sin(\frac{1}{2})} \end{gathered}[/tex]Answer:
f. False
g. True
h. False
Notice that we can correct the statements f. and h. by using the correct notation:
[tex]\begin{gathered} \text{ f. }\frac{(\sin x)^{-1}}{(\cos x)^{-1}}=(\tan x)^{-1} \\ \\ \text{ h. }(\sin x)^{-1}=\frac{1}{\sin x} \end{gathered}[/tex]describe the general trend of the unadjusted federal minimum wage from 1985 to 2020
Answers
From the graph we can infer that the general trend for the unadjusted federal minimum wage has been an increase.
Given a system of linear equations in three variables \Biggl \lbrace \begin{matrix} 4x+3y+2z=12 \\ x+y+z=9 \\ 2x+4y+3z=20 \end{matrix}
You are going to solve the system by performing the following steps.
(5pts) Eliminate y from \biggl \lbrace \begin{matrix} 4x+3y+2z=12 \\ 2x+4y+3z=20 \end{matrix}
(5pts) Eliminate y from \biggl \lbrace \begin{matrix} x+y+z=9 \\ 2x+4y+3z=20 \end{matrix}
(5pts) Eliminate x from the two equations you got from part (1) and part (2).
(2pts) Find the solution for the given system.
(3pts) Check your solution for the given system.
Answers
Answer:
Step-by-step explanation:
n
Identify the inequality or equality that describes the following situation. David drives over 9 miles per hour in the mall parking lot.
Answers
Step 1
Given; Identify the inequality or equality that describes the following situation. David drives over 9 miles per hour in the mall parking lot.
Step 2
Let x represent miles
y represents hours
Thus the inequality will be;
[tex]speed=\frac{distance}{time}[/tex][tex]\begin{gathered} Speed\text{ is over }9mph \\ This\text{ means David drives more than 9 miles per hour} \\ speed>9mph \end{gathered}[/tex]Answer; The required inequality is > or greater than because he drives over 9mph which means > 9mph
[tex]The\text{ required inequality is }>[/tex]When solving an equation for x if you get 4=10, that means what?
Answers
Given: An equation where
[tex]4=10[/tex]To Determine: the nature of the solution of the equation
Solution
Nature of solution: The example below relates to the nature of solution
[tex]\begin{gathered} Note:4=4(infinitely\text{ many solution\rparen} \\ a=4(one\text{ solution\rparen} \\ 4=10(no\text{ solution\rparen} \end{gathered}[/tex]Hence, the equation has no solution
Madison is in the business of manufacturing phones. She must pay a daily fixed cost of $400 to rent the building and equipment, and also pays a cost of $125 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
Answers
The equation that represents the total cost is C = $400 + $125p .
What is the total cost?The equation that represents the total cost is a function of the fixed cost and the variable cost. The fixed cost remains constant regardless of the level of output. The variable cost changes with the level of output.
Total cost = fixed cost + total variable cost
Total cost = fixed cost + (variable cost x total output)
C = $400 + ($125 x p)
C = $400 + $125p
Total cost when 0 phones are made = $400 + $125(0) = $400
Total cost when 1 phone are made = $400 + $125(1) = $525
Total cost when 2 phones are made = $400 + $125(2) = $650
Total cost when 3 phones are made = $400 + $125(3) = $775
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can u please help me before I get on error message, and It kicks me out the tutoring
Answers
To find the image we have to multiply every coordinate by the scale factor.
Then:
[tex]\begin{gathered} A^{\prime}(0,2) \\ B^{\prime}(9,0) \\ C^{\prime}(4,4) \end{gathered}[/tex]ANSWERRRRRRRRRRRRRRRRRRRRRRR
Answers
The perimeter of the figure is 22.4 cm, and The area of the figure is 30.2cm²
What is meant by Pythagoras connection?The Pythagorean theorem, or Pythagorean theorem, explains the relationship between the three sides of a right-angled triangle. The square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle, according to Pythagoras' theorem.
From the diagram, the formation is a rectangle.
Use the coordinate points to find the measurements of each side.
Side length AD = Side length BC
Apply the Pythagoras connection to find length BC as;
a² + b²= c² where a=2 cm and b = 4 cm and c =BC
2² + 4² = c²
4+16 = c²
20 = c²
c= √20 = 4.4721
Length BC = Length AD = 4.5 cm
Side length AB = Side length DC
Apply the Pythagoras connection to find the length DC as;
a² + b²= c² where a=6 cm and b = 3 cm and c =DC
6² + 3² =c²
36 + 9 = c²
45 = c²
√45 = c
c= 6.7082
c = DC = 6.7 cm
Now you have the dimensions of the rectangle as;
Length = 6.7 cm and width = 4.5 cm
The perimeter will be ;
P= 2{l +w} --------- where l is length and w is width and P is the perimeter of the rectangle
P=2{6.7 + 4.5}
P=2{11.2}
P= 22.4 cm
The area will be ;
A= l*w
A= 6.7 * 4.5 = 30.15 = 30.2 cm²
The perimeter of the figure is: 22.4 cm
The area of the figure is: 30.2 cm²
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A bag contains 42 red, 42 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is purple or not red
Answers
The probability of a candy when randomly taken is purple or not red is 0.235
Given,
Number of red candies in the bag = 42
Number of green candies in the bag = 42
Number of yellow candies in the bag = 20
Number of purple candies in the bag = 32
We have to find the probability of a candy when randomly taken is purple or not red.
Probability, P(E) = Number of favorable outcomes / Total number of favorable outcomes
Here,
Number of favorable outcomes = 32
Total number of favorable outcomes = 42 + 42 + 20 + 32 = 136
So,
P(E) = 32/136 = 0.235
That is,
The probability of a candy when randomly taken is purple or not red is 0.235
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An object moves according to a law of motion, where, its position is described by the following function, s = f(t) = t^4 - 4t + 1. The time t is measured in seconds and s in meter.a. Sketch the velocity graph and determine when is the object moving in the positivedirection.b. Draw a diagram of the motion of the object and determine the total distancetraveled during the first 6 seconds.
Answers
SOLUTION
(a) The function given is the distance graph. The velocity fuction is the derivative of the distance function. This becomes
[tex]\begin{gathered} f(t)=t^4-4t+1 \\ f^{\prime}(t)=4t^3-4 \\ v=4t^3-4 \end{gathered}[/tex]the graph is shown below
From the velocity graph above, the function is moving in a positive direction from 1 second and beyond
(b) The diagram of motion of the object is shown in the distance graph below
The total distance travelled is the integral of the velocity function from 0 to 6 as shown below
[tex]\begin{gathered} \int_0^64x^3-4 \\ =[\frac{4x^4}{4}-4x]_0^6 \\ =[x^4-4x]_0^6=6^4-4(6)-(0^4-4(0)) \\ =1296-24-0 \\ =1272 \end{gathered}[/tex]Hence the answer is 1272 m
Which of the following could be the end behavior of f(x) = -x2 – 4?
Answers
Answer:
f(x) = -∞ as x → ±∞
Explanation:
The given function is
f(x) = -x² - 4
To know the end behavior, let's replace x by a greater number and by a smaller number, so
If x = 100
f(x) = -100² - 4
f(x) = -10000 - 4
f(x) = -10004
If x = -100
f(x) = -(-100)² - 4
f(x) = -10000 - 4
f(x) = -10004
So, we can see that no matter if x is negative or positive, the value of f(x) will be positive. Then, we can say that the end behavior is
f(x) = -∞ as x → ±∞
1 yard =3 feet1 meter= 100 cmNicholas walked 20 yards to get his mail. About how many meters did he walk?
Answers
Given:
1 yard = 3 feet
1 meter = 100 cm
Nicholas walked 20 yards to get his mail.
Here, we are required to convert 20 yards to meters.
Where,
1 yard = 0.9144 meter
20 yards = x meters
thus, we have:
[tex]20\text{ }\times0.9144\text{ = 18.29 meters}[/tex]Therefore, Nicholas walked 18.29 meters to get to his mail.
ANSWER:
18.29 meters
The perimeter of a triangle is 19 inches. One side measures 7 inches. Another side is 5 inches long.Find the length of the third side c.
Answers
Statement Problem: The perimeter of a triangle is 19 inches. One side measures 7 inches. Another side is 5 inches long.
Find the length of the third side c.
Solution:
Thus, the perimeter of a triangle with lengths a, b and c is;
[tex]P=a+b+c[/tex][tex]\begin{gathered} \text{Let a=7inches, b=5inches, P=19inches} \\ c=P-a-b \end{gathered}[/tex]Thus, we have;
[tex]\begin{gathered} c=19-7-5 \\ c=7 \end{gathered}[/tex]Thus, the length of the third side is 7inches