The number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed is 243.
According to the given question.
The total number of elements, n = 3
The number of elements to be selected at a time when repetition is allowed, r = 5
Since, we know that " the number of ways or permutations of n things taken r all at a time, when repetition of things are allowed, is [tex]n^{r}[/tex].
Therefore,
The number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed
= [tex]3^{5}[/tex]
= 243
Hence, the number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed is 243.
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A cube shaped box has a side length of 15 inches and contains 27 identical cube shaped blocks. what is the surface area of all 27 blocks compared to the surface area of the box?
The surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.
What is a cube?A cube is a three-dimensional solid object with six square faces, facets, or sides, three of which meet at each vertex.To find the total surface area of the 27 blocks:
A cube's surface area
SA = 6s² (where s is the side length)Given that the box's side length is 15 inches:
SA of box = 6152 = 1350 in2Surface Area of 3-inch side length blocks:
⇒ SA = 6 · 3² = 54 in²27 blocks SA = 27 54 = 1458 in2Surface Area of 4-inch side length blocks:
⇒ SA = 6 · 4² = 96 in²27 96 = 2592 in2 SA of 27 blocksSurface Area of 5-inch side length blocks:
⇒ SA = 6 · 5² = 150 in²27 blocks SA = 27 150 = 4050 in2Therefore, from the given answer options for the total surface area of the 27 blocks, the side length of the blocks must be 5 inches.
To calculate how many times the total surface area of the 27 blocks is to the surface area of the box:
So,
The side length of the blocks is 5 inches.
The total surface area of the 27 blocks is 4050 square inches.
This is 3 times the surface area of the box.
Therefore, the surface area of all 27 blocks compared to the surface area of the box is 3 times the surface area of the box.
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Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep, and the angle between the sloping sides is 77°. What is the shortest distance between the tip of the cone and its rim?
177.8 centimeters.
What is the formula for cos θ?The symbol for it is Cosθ, and it has the following form: adjacent/hypotenuse = cosθ. In other words, it divides the length of the hypotenuse by the length of the neighboring side, which is the side next to the angle (the longest side of a right triangle).When working with right-angled triangles, the Cos Theta Formula is particularly helpful. The Cosine of an angle in a right triangle is always equal to the hypotenuse's length divided by the length of the neighboring side. This makes it an excellent tool for resolving Cosine-related issues.The shortest distance between the tip of the cone and its rim:
cos θ= base/Hypotenuse
cos 77°=[tex]\frac{40}{H}[/tex]
[tex]0.22495=\frac{40}{H}[/tex]
[tex]H=177.8[/tex]
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The shortest distance between the tip of the cone and its rim exits 51.11cm.
What is the shortest distance between the tip of the cone and its rim?If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.
Cos 38.5 = 40 / x
Solving the value of x, we get
Multiply both sides by x
[tex]$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x[/tex]
[tex]$\cos \left(38.5^{\circ}\right) x=40[/tex]
Divide both sides by [tex]$\cos \left(38.5^{\circ}\right)$[/tex]
[tex]$\frac{\cos \left(38.5^{\circ}\right) x}{\cos \left(38.5^{\circ}\right)}=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]
simplifying the above equation, we get
[tex]$x=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]
x = 51.11cm
The shortest distance between the tip of the cone and its rim exits 51.11cm.
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Quick algebra 1 question for some points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]let \: the \: number \: be \: denoted \: by \: p \\ five \: times \: a \: number = 5p \\ square\: of \: a \: number = p {}^{2} [/tex]
[tex] \gamma - p {}^{2} = 5p - p {}^{2} [/tex]
particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 14t + 85, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?
The constant in the expression represents that the company earned 85 billion dollars in 2008.
What does the constant represent?The expression given in the question is known as a quadratic function. A quadratic function is a function that usually has a single variable and it is raised to the power of 2. The graph of a quadratic function is a curve called a parabola. Parabolas may curve upward or downward
An example of a quadratic function is ax² + bx + c
Where: a,b, c are real numbers not equal to zero
c = constant.
The constant in this question is 85. It is the amount earned in 2008
Here are the options:
The company earned 85 billion dollars from 2008 to 2018
The company earned 85 billion dollars in 2008
The company earned 14 billion dollars from 2008 to 2018.
The company earned 14 billion dollars in 2008.
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What is the constant of variation for the following table? If your answer is in the form of a fraction, write your answer in as a/b.
(where a is the numerator and b is the denominator)
Answer:
1/4
Step-by-step explanation:
Change is y (f9x) over the change in x.
Look at the f(x) column.
What is the change from -2 to -1? 1
What is the change from -1 to 0? 1
What is the change from 0 to 1? 1
What is the change from 1 to 2? 1
We see that this change is constant. It is always 1.
Look at the x column.
What is the change from -8 to -4? 4
What is the change from -4 to 0? 4
What is the change from 0 to 4? 4
What is the change from 4 to 8? 4
We see that the change is constant. It is always 1.
When we put this change the form a/b we get 1/4
Which values below belong in this table? Select all that apply.
The possible value of y are 16, 32 and 64
How to find the values of an exponential table?The table above is an exponential table.
Therefore, let's confirm the ratio of the y axis.
8 / 4 = 2
4 / 2 = 2
Therefore, the other y axis can be gotten as follows:
y = 8 × 2 = 16
y = 16 × 2 = 32
y = 32 × 2 = 64
y = 64 × 2 = 128
Therefore, the possible value of y are 16, 32 and 64
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Elena reflects the word 'MOM' over the x-axis and finds that it makes a new word. What is the new word?
A grandfather's age in years is the same as his granddaughter's age is months. Together, they are 91 years old. How old is the grandfather?
Answer:
Step-by-step explanation:
It cost Taub $5.00 to send 100 text messages. How many text messages did she send if she spent $9.55
[tex]\begin{array}{ccll} \$&messages\\ \cline{1-2} 5 & 100\\ 9.55& x \end{array} \implies \cfrac{5}{9.55}~~=~~\cfrac{100}{x} \\\\\\ 5x=955\implies x=\cfrac{955}{5}\implies x = 191[/tex]
The number of text messages that can be sent with $9.55 is 191.
Given that, it cost Taub $5.00 to send 100 text messages.
We need to find how many text messages did she send if she spent $9.55.
What is the proportion?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the number of text messages she sent with $9.55.
Now, 5:100::9.55:x
⇒5x=955
⇒x=955/5
⇒x=191
Therefore, the number of text messages that can be sent with $9.55 is 191.
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Franco has enough paint to cover an area of approximately 226 square feet. he needs to paint a cylinder that is 5 feet long. what is the maximum possible radius of the cylinder that can be covered by the paint?
The required radius of the cylinder that can be covered by the paint exists at 3.8 feet.
Franco has enough paint to protect an area of about 226 square feet. He must paint a cylinder that exists 5 feet, and the maximum possible radius of the cylinder that can be covered by the paint exists to be determined.
What is a cylinder?The cylinder exists described as a 3D solid that holds two identical bases joined by a curved surface, at a particular distance.
Here, Franco keeps sufficiently paint to cover an area of about 226 square feet.
Area of the cylinder = 226
Area of the cylinder = πr²h = 226
h = 5 feet and π = 3.14
3.14 [tex]*[/tex] 5 [tex]*[/tex] r² = 226
r² = 226/15.70
[tex]$r = \sqrt{14.70}[/tex]
r = 3.80
Therefore, the required radius of the cylinder that can be covered by the paint exists at 3.8 feet.
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Answer: 4
Step-by-step explanation: I got the answer 4 right on the test
There 13 yellow cards, 6 blue, 10 red, 8 green cards in a stack of cards turned face down. Once a card is selected, it is not replaced. Find P(2 blue cards). Please be specific with your answer.
Answer:
5/222
Step-by-step explanation:
you need to add all the cards together first
13 + 10 + 8 + 6 = 37
then you take out 1 card to find the first probability of the blue card (there are 6 blue cards out of 37)
so 6/37
that will be your first probability
then for the 2nd probability, you will have 1 less card grom the deck making it only 36 cards (after taking out the first one, there will be only 5 blue cards left)
making it 5/36
that will be the 2nd probability
then you multiply both these probabilities to find the answer
6/37 × 5/36 = 5/222
Which elementary row operation will reduce the x–element in row 2 to 0 in this matrix?
The elementary row operation that will reduce the x–element in row 2 to 0 in this matrix is -2R1 + R2
How to determine the elementary row operation?The complete question is added as an attachment
The matrix is given as:
1 1 1 12
2 1 0 14
2 0 3 19
Rewrite as:
x y z
1 1 1 12
2 1 0 14
2 0 3 19
So, the x-element of the second row is
x = 2
When the first row is multiplied by negative 2 and added to the second row, the x-element of the second row is reduced to 0
This is represented as;
-2R1 + R2
i.e.
-2(1 1 1 12)
+ 2 1 0 14
---------------------------
0 -1 -2 -10
Hence, the elementary row operation that will reduce the x–element in row 2 to 0 in this matrix is -2R1 + R2
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Which function displays this end behavior
- As x approaches negative infinity, y approaches positive infinity.
- As x approaches positive infinity, y approaches negative infinity.
Step-by-step explanation:
Since you haven't provided any functions, I can answer this question generally as to what the function would look like.
So when a polynomial has an even degree, then the two end behaviors will go in the same direction, and when it has an odd degree, then the two end behaviors will be in opposite directions. When a polynomial has a positive leading coefficient the right side will go towards infinity, and if a polynomial has a negative leading coefficient the right side will go towards negative infinity.
So let's look at the information:
As x approaches negative infinity, y approaches positive infinity.
Just given this we can't really say anything about the polynomial since we have to relate this to the right end behavior, or as x approaches infinity, so let's look at that.
As x approaches positive infinity, y approaches negative infinity.
This means that as x increases, y decreases, so that means the leading coefficient is negative. Since we know both end behaviors, and they're opposite (one y-value goes to negative infinity, and the other positive infinity), that means the polynomial is an odd degree.
So this means the polynomial will look something like this:
[tex]ax^n+bx^{n-1}+cx^{n-2}...[/tex]
where the leading coefficient "a" is negative and the degree of the polynomial (degree of leading coefficient) will be odd.
Answer:A
Step-by-step explanation:
edge 2023
Put in decimal form, out to the nearest hundredth and explain how you got your answer.
This problem is meant to be done in order of operations.
Answer: [tex]\Large\boxed{2}[/tex]
Concept:
Here, we need to know the idea of the PEMDAS method.
PEMDAS is an acronym for the order of operations.
ParenthesisExponentsMultiplicationDivisionAdditionSubtractionSolve:
Given expression
[tex]\dfrac{3^3~-~13}{11~-~2^2}[/tex]
Simplify the exponents
[tex]=\dfrac{27~-~13}{11~-~4}[/tex]
Simplify by subtraction
[tex]=\dfrac{14}{7}[/tex]
Simplify the fraction
[tex]\Large\boxed{=2}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Which of the following statements does not describe a characteristic of the line of best fit for a scatter plot?
I'll go for the third option. It seems sensible to having a balance in estimating provided data, even though that may not always be the case.
Hope this helps!
Type the correct answer in each box. use numerals instead of words. the surface area of a cylinder is approximately 640.56 square meters. the radius of the cylinder is 5 meters less than the height of the cylinder. to the nearest whole meter, what are the radius and height of the cylinder? the radius is approximately meters, and the height is approximately meters.
The radius of cylinder = 6 meter
The height of cylinder = 11 meter
According to the question,
Surface area of the cylinder = 640.56 m²
Let the height of the cylinder = x meters
Let the radius of the cylinder = (x-5)meters
Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)
640.56 = 2 (3.14) (x-5) (x)
640.56/(6.28) = x² - 5x
x² - 5x =102
x² - 5x - 102 =0
using quadratic equation, [-b±√(b² - 4ac)]/2a.
b = -5; a=1; c=102
x =[-(-5) ±√(-5)² - 4(1)(102)]/2
= [5 ± √433]/2
x = 11 and -7
since x=-7 neglect negative value, we get x=11.
The height of the cylinder is 11 meters
The radius of the cylinder is (11 - 5) = 6 meters.
Hence, The radius of cylinder = 6 meter.
The height of cylinder = 11 meter.
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Answer:
Step-by-step explanation:
The radius of cylinder = 6 meter
The height of cylinder = 11 meter
According to the question,
Surface area of the cylinder = 640.56 m²
Let the height of the cylinder = x meters
Let the radius of the cylinder = (x-5)meters
Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)
640.56 = 2 (3.14) (x-5) (x)
640.56/(6.28) = x² - 5x
x² - 5x =102
x² - 5x - 102 =0
using quadratic equation, [-b±√(b² - 4ac)]/2a.
b = -5; a=1; c=102
x =[-(-5) ±√(-5)² - 4(1)(102)]/2
= [5 ± √433]/2
x = 11 and -7
since x=-7 neglect negative value, we get x=11.
The height of the cylinder is 11 meters
The radius of the cylinder is (11 - 5) = 6 meters.
Hence, The radius of cylinder = 6 meter.
The height of cylinder = 11 meter.
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i want to solve this problem i forgot maths lol 4/5 + 8/5
Answer:
The correct answer is 2 [tex]\frac{2}{5}[/tex].
Step-by-step explanation:
To get this answer, we first have to add the numerators.
We can easily say that 4 + 8 = 12
That leaves us with the improper fraction, [tex]\frac{12}{5}[/tex].
To make this fraction proper, we must first find out how many times 5 can go into 12.
5 can go into 12 two times which leaves us with 2 left over from the numerator.
Now all that's left to do is add 2 (the amount of times 5 can go into 12) and [tex]\frac{2}{5}[/tex] (the left over fraction) to get the answer 2[tex]\frac{2}{5}[/tex].
Hope this helps:) Goodluck!
Area=
Help me please thanks :)
Answer:
16 square units
Step-by-step explanation:
You find the area by multiplying the base times the height. The base or horizonal length is 4. You get this from the ordered point x (4,0). The x coordinate 4, tells us that the point x is 4 spaces to the right of zero, so the length or base is 4.
The height is also 4. You get this from the point S (2,4) The y coordinate of 4 tells you how high up the point is.
4 x 4 = 16
The likelihood of the frequency of an event in repeated trials under similar conditions is?
The probability of the frequency of an event in repeated trials under comparable circumstances is a statistical analysis.
What is Statistical analysis?The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.
What accomplishes statistical analysis?Finding the distribution hidden in your data is the aim of a statistical analysis. What do you mean by the distribution that lies underlying my data? "The distribution of your data describes the peaks and valleys of its characteristics in relation to a target population.
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Which graph represents a reflection across the x-axis of g(x) = Three-fourths(3)x?
See attached images for the graph.
The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $8.50, and bags of cookies cost $4.50, and sales equaled $79.00 in total. There were 6 more bags of cookies than candy sold.
Find the number of bags of candy and cookies sold by the drama club. Show your work.
The number of bags of candy and cookies sold by the drama club is 4 and 10 respectively
Simultaneous equationlet
number of bags of candy = xnumber of bags of cookies = yThe equation:
8.50x + 4.50y = 79
y = x + 6
Substitute x = y + x into
8.50x + 4.50y = 79
8.50x + 4.50(x + 6) = 79
8.50x + 4.50x + 27 = 79
8.50x + 4.50x = 79 - 27
13x = 52
x = 52/13
x = 4
Recall,
y = x + 6
y = 4 + 6
y = 10
Therefore, the number of bags of candy and cookies sold by the drama club is 4 and 10 respectively.
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"if i purchase this product for $79.99 and two accessories for $9.99 and $7.00, how much would i owe after the 8.75% tax is applied?" employee: "your total would be __________."
Answer:$96.98
Step-by-step explanation: all you just do is to add it all up to the total amount.
Answer: $105.47
I hope you get the job!!!!!
Question 3
What's the height of a cone if the volume is 562 cubic inches and the radius is 5 inches.
O 72.05 units
O 120.62 units
O21.47 units
O38.90 units
Previous
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=562\\ r=5 \end{cases}\implies 562=\cfrac{\pi (5)^2 h}{3}\implies 1686=25\pi h \\\\\\ \cfrac{1686}{25\pi }=h\implies 21.47\approx h[/tex]
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex] \sqrt{112x {}^{6}y {}^{3} {z}^{5} } \\ \sqrt{(2 {}^{4} \times 7 )x {}^{6}y {}^{2}yz {}^{4} z } \\ 2 {}^{2}x {}^{3} yz {}^{2} \sqrt{7yz} [/tex]
Last optionHere are the scores of 14 students on a geography test. 58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87 Notice that the scores are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range
Answer:
58, 66, 79, 84, 87 (see explanation for the exact answer)
Step-by-step explanation:
{58, 66, 79, 84, 87}
minimum = 58
lower quartile = 66
median = 79
upper quartile = 84
maximum = 87
Answer + Step-by-step explanation:
58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87
The data set is in order then :
the minimum = 58
The maximum = 87
Determining the median :
first ,we notice that the data set has an even number (14) of numbers
Then
The median is the average of the two central values of the data set :
the two central values are the 7th and 8th numbers:
[tex]\text{median} =\frac{79+79}{2} =79[/tex]
Determining the lower quartile :
The lower quartile is the median of the set :
58, 60, 65, 67 , 68, 72, 79
this set has an odd number (7) of values
Then
The central value is 67
Therefore
The lower quartile is 67
Determining the upper quartile :
The upper quartile is the median of the set :
79, 80, 81, 82 , 86, 86, 87
this set has an odd number (7) of values
Then
The central value is the 4th number which is 82
Therefore
The upper quartile is 82
Interquartile range :
82 - 67 = 15
The price of a television was reduced from 250 to 200. by what percentage was the price of the television reduced
Answer:
20%
Step-by-step explanation:
We can start by finding out how much the price of the television was reduced by.
250 - 200 = 50
Now, we need to know what percent of 250 is 50? Let x represent the percent of 250 that is 50. Using this, we can set up an equation:
[tex]x\%\times 250=50[/tex]
Notice that a percentage can also be written as that number over 100.
[tex]\frac{x}{100}\times250=50[/tex]
[tex]\frac{250x}{100}=50[/tex]
Reduce the fraction (250 and 100 have a common factor of 10)
[tex]\frac{25x}{10}=50[/tex]
Reduce the fraction again (25 and 10 have a common factor of 5)
[tex]\frac{5x}{2}=50[/tex]
Multiply both sides by two
[tex]5x=100[/tex]
Divide both sides by 5
[tex]x=20[/tex]
Therefore the price of the television was reduced by 20%.
The linear density in a rod 5 m long is 10 x + 4 kg/m, where x is measured in meters from one end of the rod. Find the average density ave (in kg/m) of the rod.
The average density of the rod is 0.704 kg/m.
For given question,
We have been given the linear density in a rod 5 m long is 10 / x + 4 kg/m, where x is measured in meters from one end of the rod.
We need to find the
The length of rod is, L = 5 m.
The linear density of rod is, ρ = 10/( x + 4) kg/m
To find the average density we need to integrate the linear density from x₁ = 0 to x₂ = 5,
The expression for the average density is given as,
⇒ ρ'
[tex]=\int\limits^5_0 {\rho} \, dx\\\\=\int\limits^5_0 {\frac{m}{L} } \, dx\\\\=\int\limits^5_0 {\frac{10}{5(x+4)} }\, dx\\\\=\int\limits^5_0 {\frac{2}{x+4} }\, dx[/tex] ......................(1)
Using u = x + 4
du = dx
u₁ = x₁ + 4
u₁ = 0 + 4
u₁ = 4
and
u₂ = x₂ + 4
u₂ = 5 + 4
u₂ = 9
By entering the values above into (1), we have:
⇒ ρ'
[tex]=2\int\limits^9_4 {\frac{1}{u} } \, du\\\\ = 2[(log~u)]_4^{9}\\\\=2[(log~9-log~4)]\\\\=2\times[0.352][/tex]
= 0.704
Thus, we can conclude that the average density of the rod is 0.704 kg/m.
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Geometry: complete this proof (ASAP!!! It’s urgent)
Answer:
1. BD bisects <CBE, AE || BD (Given)
2. <EBD ~= <CBD (Definition of < Bisectors)
3. <AEB ~= <EBD (Alternate Interior Angles Theorem)
4. <CAE ~= <CBD (Corresponding Angles Postulate)
5. <CAE ~= <AEB (Transitive Property of Congruence)
6. AB ~= BE (Converse of Isosceles Triangles Theorem)
help pleaseee and explain how , I’m confused thanks
Answer:
The rope is worth 13.
The shoe is worth 5.
The clock is worth 3.
Step-by-step explanation:
We know that the weights are 8 so we will use 8 for the weights.
Let s = show
Let r = rope
Let c = clock
We have three unknowns so we need three equations.
8 + s = r c + s = 8 s= c +2
There are a number of ways that we can approach this. Let's substitute
c + 2 for s in the first 2 equations.
8 + s = r
8 + c + 2 = r
10 + c = r
c + s = 8
c + c + 2 = 8
2c + 2 = 8
2c = 6
c = 3 we found the value of the clock.
Now, let's substitute 3 in for 3 in the bold equation above.
10 + c = r
10 + 3 = r
13 = r we found the value of the rope.
We can use any of the equations to find the shoe.
s= c + 2
s = 3 + 2
s = 5
This is tricky. It takes a lot of practice. Don't give up!
Shoe= 5
Rope= 13
Clock= 3
We can start by giving each item a variable. Shoe= s, rope= r, clock= c. The weight is 8, so we don't need to give it a variable. Our equations are now:
8+s= r
c+s= 8
s= c+2
Now, we can isolate a variable to solve for it using the substitution method. Let's start with s.
c+s=8
-c -c
s= 8-c
Now, we'll take another equation and plug s in.
8-c=c+2
+c +c
8= 2c+2
-2 -2
6=2c
c=3
Now we know that the clock is 3. Put 3 into the last equation, and add 3+2 to get 5 for the shoe. 5 in the first equation for the shoe plus 8 as the weight means the rope is 13.
hope this helped!
Three fair, standard six-faced dice of different colors are rolled. In how many ways can
the dice be rolled such that the sum of the numbers rolled is 15?
These are some of the ways you can make 15 by adding three numbers together.
The first way is doing 6+6+3.There are some more ways to do it too.
2nd way is 6+4+5.
3. 1+6+6
4. 5+5+5
