Please reference attached image for the problem that requires solving. Thank you so much for taking the time to help.
Answers
Explanation:
The number of times the 6-sided number cube will be rolled will is
[tex]750[/tex]Let the numbers greater than 4 be represented below as
[tex]E_1[/tex][tex]\begin{gathered} E_1=\lbrace5,6\rbrace \\ n(E_1)=2 \end{gathered}[/tex]The number of sample space will be
[tex]n(S)=6[/tex]The probability of rolling a number greater than 4 will be calculated below as
[tex]\begin{gathered} Pr(E_1)=\frac{n(E_1)}{n(S)} \\ Pr(E_1)=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]Hence,
To calculate the number of times a number greater than 4 will be rolled will be calculated below as
[tex]\begin{gathered} =Pr(E_1)\times750 \\ =\frac{1}{3}\times750 \\ =250times \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow250\text{ }times[/tex]Related Questions
2 - 2f(x)X + 1g(x) = 18 - 3.2Escreva (fog)(2) como uma expressão em função de 2.(fog)(x) =
Answers
Answer
[tex](f\text{ o g)(x) = }\frac{3x-16}{17-3x}[/tex]Explanation
We are given that
f(x) = (2 - x)/(x + 1)
g(x) = 18 - 3x
We are then asked to find (f o g)(x)
(f o g) (x) is the same as writing the expression for f(x) but instead of x, we will write g(x) in the expression.
[tex]\begin{gathered} f(x)=\frac{2-x}{x+1} \\ (\text{fog)(x) = }\frac{2-g(x)}{g(x)+1} \end{gathered}[/tex]Recall that
g(x) = 18 - 3x
So,
[tex]\begin{gathered} (\text{fog)(x) = }\frac{2-g(x)}{g(x)+1} \\ (\text{f o g)(x) = }\frac{2-(18-3x)}{18-3x+1} \\ (f\text{ o g)(x) = }\frac{2-18+3x}{17-3x} \\ (f\text{ o g)(x) = }\frac{-16+3x}{17-3x} \\ (f\text{ o g)(x) = }\frac{3x-16}{17-3x} \end{gathered}[/tex]Hope this Helps!!!
A hexagonal prism whose base has area 25.6 square centimeters and who’s height is 8.9 centimeters
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We are given the following information about a hexagonal prism.
Base area = 25.6 cm²
Height = 8.9 cm
Recall that the volume is given by
[tex]V=B\cdot h[/tex]Where B is the area of the base and h is the height of the hexagonal prism.
Let us substitute the given values into the above formula
[tex]\begin{gathered} V=B\cdot h \\ V=25.6\cdot8.9 \\ V=227.84\: cm^3 \end{gathered}[/tex]Therefore, the volume of the given hexagonal prism is 227.84 cubic centimeters.
What is the image point of (-2,-3) after a translation right 2 units and up 4 units?
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The figure below is the graph of the dimensions of a rectangle whoseadjacent side lengths exhibit direct variation.
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Concept
What is a direct variation? A direct variation is a direct relationship between two variables in which increase in one variable lead to increase in the other variable and decrease in one variable lead to decrease in the other variable.
Hence, the relationship fron the graph between Height and Width of the rectangle is not a direct variation.
Therefore,
The relationship is not a direct variation.
Final answer
Option B = False
3. A data set has six numbers. Four of the numbers are: 4, 3, 8, 12. If the mode is 3, find at least three possibilities for the other two numbers.
Answers
The possibility of the other two numbers in the given data set is 3.
What do we mean by a number?An object that can be counted, measured, and given a name is a number. The initial examples are the natural numbers 1, 2, 3, 4, and so forth. In language, numbers can be expressed using number words. The symbols referred to as numerals can be used to represent specific numbers in a more general way; for instance, the numeral "5" stands for the number five. Due to the limited amount of symbols that can be learned, fundamental numbers are typically arranged in a numeral system, which is a systematic manner of representing any number. The Hindu-Arabic numeral system, which enables any number to be expressed using a combination of 10 fundamental numeric symbols known as digits, is the most widely used numeral system.So, by observing the data, we can simply conclude that:
As the mode is 3, the remaining two numbers are 3.Therefore, the possibility of the other two numbers in the given data set is 3.
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Hey can you pleas help me on this math problem thank you
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Given:
Nolan wraps 36 presents in 12 hours on Saturday
And wraps 42 presents in 14 hours on Friday
If y = number of gifts, and x = number of hours
So, the proportional equation will be as follows:
[tex]y=kx[/tex]Where k is the constant of proportionality
Total gifts = y = 36 + 42 = 78
Total hours = x = 12 + 14 = 26
So, subtitute into the euation to find k
[tex]\begin{gathered} 78=k\cdot26 \\ k=\frac{78}{26}=3 \end{gathered}[/tex]So, the answer will be the constant = 3
Marsha buys 3 pounds of cheddar cheese and some Swiss cheese Both cheeses cost $450 per pound. The total cost is $24.75. How many pounds of Swiss cheese did Marsha buy?
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Let x represent the number of pounds of Swiss cheese that Marsha bought.
We were told that Marsha buys 3 pounds of cheddar cheese and some Swiss cheese Both cheeses cost $450 per pound. This means that the cost of 3 pounds of cheddar cheese is 3 * 4.50 = 13.5
Also, the cost of x pounds of Swiss cheese is 4.5 * x = 4.5x
If the total cost is $24.75, it means that
4.5x + 13.5 = 24.75
The equation is
4.5x + 13.5 = 24.75
We would solve for x. Thus,
4.5x = 24.75 - 13.5
4.5x = 11.25
x = 11.25/4.5
x = 2.5
Thus, she bought 2.5 pounds of Swiss cheese
help;aaefefdsfsd fnujyhvbnmhgf rfdgtrbtg get it?
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The value of the expression [tex]\frac{-4[5(7-13)-19]}{2(-1)}[/tex] is - 98.
The abbreviation BODMAS rule is used to assist kids to recall the proper order of operations when performing mathematics. Operations are essentially the various mathematic operations we can do on numbers. "Brackets, Order, Division, Multiplication, Addition, Subtraction" is what it stands for.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Consider the expression,
[tex]\frac{-4[5(7-13)-19]}{2(-1)}[/tex]
Using the BODMAS rule,
We will first solve the parenthesis.
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-4[35-65-19]}{-2}[/tex]
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-140+260+76}{-2}[/tex]
Now, the next step is to divide the expression.
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=\frac{-140}{-2}+\frac{260}{-2}+\frac{76}{-2}[/tex]
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=70-130-38[/tex]
Subtracting the expression,
[tex]\frac{-4[5(7-13)-19]}{2(-1)}=-98[/tex]
Hence, the value of the expression is - 98.
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What is the slope of the following equation? -3y-x=0
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Given the equation
[tex]-3y-x=0[/tex]To determine the slope, first write the equation in slope-intercept form (y=mx+b)
[tex]\begin{gathered} -3y-x=0 \\ -3y=x \\ y=-\frac{1}{3}x \end{gathered}[/tex]The slope corresponds to the coefficient multiplying x.
For this equation the slope is equal to -1/3.
Consider a trebuchet launching a flaming stone over a castle wall. It is mounted on a small hill and has a parabolic trajectory (neglecting air resistance). Once it crashes into the ground on the other side of the castle wall, it comes to rest. This motion is described by the function below, where x, measured in meters, represents horizontal displacement from the launch position and y = f(x) represents vertical distance from the ground, measured in meters.
f(x) = -0.25x2 + 3.15x + 5
Determine the contextual domain and range and justify your answers. What is the peak height of the flaming stone?
Answers
The domain of function f(x) is the set of all real numbers.
the range of function f(x) is, f ≤ 14.9225
And the peak height of the flaming stone would be, 14.9 meters
In this question, we have been given a trebuchet launching a flaming stone over a castle wall. It is mounted on a small hill and has a parabolic trajectory. Once it crashes into the ground on the other side of the castle wall, it comes to rest. This motion is described by the function f(x) = -0.25x² + 3.15x + 5, where x, measured in meters, represents horizontal displacement from the launch position and y = f(x) represents vertical distance from the ground, measured in meters.
We need to determine the contextual domain and range and justify your answers.
The domain of function f(x) is the set of all real numbers.
The range of function f(x) is, f ≤ 14.9225
From the range of the function, the peak height of the flaming stone would be, 14.9 meters
Therefore, the domain of function f(x) is the set of all real numbers.
the range of function f(x) is, f ≤ 14.9225
And the peak height of the flaming stone would be, 14.9 meters
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Try this: Find "y." How does CPCTC help? A ABC EA ADC. Find y. A (3y) 21° D C С B. DO Pear Deck Interacti Do nove Students, enter a number!
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AS ACD and ACBare congruent triangles, we have that
[tex]\begin{gathered} 3y=21\rightarrow \\ y=\frac{21}{3}=7 \end{gathered}[/tex]so the answer is y=7
An ice cream shop owner's business assets and liabilities are listed below. Owned Inventory $32,500 Cash $75,420 Building Mortgage $154,265 Savings Account $25,000 Owned Equipment $15,670 Small Business Loan $15,652 Other Debt $1,235 Accounts Receivable $12,540 Property Value $125,768 What is the total value of the ice cream shop owner's business assets? $125,768 $171,152 $274,358 $286,898
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The total value of the ice cream shop owner's business assets is D. $286,898.
What are business assets?Business assets are the value of the assets of the Ice Cream Shop.
Business assets are distinct from the owner's assets.
The business assets consist of liabilities (amounts owed outsiders) and equity (the difference between assets and liabilities).
Business Assets:Owned Inventory $32,500
Cash $75,420
Savings Account $25,000
Owned Equipment $15,670
Accounts Receivable $12,540
Property Value $125,768
Total assets = $286,898
Business Liabilities:Small Business Loan $15,652
Other Debt $1,235
Building Mortgage $154,265
Total liabilities = $171,152
Equity = $115,746 ($286,898 - $171,152)
Thus, the business assets for this ice cream shop are worth Option D.
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The triangle ABC pictured below is a right, isosceles triangle. If the length of side AC is 3, give the lengths of the other two sides and the measures of angle A and angle B.
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From the statement, we know that we have a right triangle that:
0. has an angle ∠C = 90°,
,1. is also an isosceles triangle,
,2. has a side AC = 3.
1) From points 2 and 3, we know that:
[tex]AC=BC=3.[/tex]Because we have a right triangle, we can use Pitagoras Theorem, which states that:
[tex]c^2=a^2+b^2.[/tex]Where:
• c = AB = hypotenuse,
,• a = BC = 3,
,• b = AC = 3.
Replacing these data in the equation above, we get:
[tex]c^2=3^2+3^2=9+9=18\Rightarrow AB=c=\sqrt{18}.[/tex]2) From point 2 we know that angles A and B must be equal:
[tex]\angle A=\angle B.[/tex]From geometry, we know that the inner angles of a triangle sum up to 180°, so we have:
[tex]\angle A+\angle B+\angle C=180\degree\Rightarrow2\angle A+\angle C=180\degree\Rightarrow\angle A=\frac{180\degree-\angle C}{2}=\frac{180\degree-90\degree}{2}=45\degree.[/tex]Where we have used point 1.
AnswerThe sides of the triangle are:
• AB = √18,,
,• AC = 3,
,• BC = 3.
The angles of the triangle are:
• ∠A = 45°,,
,• ∠B = 45°,,
,• ∠C = 90°.
A college student completed some courses worth 6 credits and some courses worth 4 credits. The student earned a total of 104 credits after completing 21 courses.How many courses worth 4 credits did the student complete?A. 11B. 26C. 13 D. 10
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Let x be the number of four credit courses and let y be the number of six credit courses.
We know that the student have completed 21 courses, this means that:
[tex]x+y=21[/tex]We also know that he has 104 credits in total. This means that:
[tex]4x+6y=104[/tex]Then we have the system of equations:
[tex]\begin{gathered} x+y=21 \\ 4x+6y=104 \end{gathered}[/tex]To solve the system we solve the first equation for y and plug the value in the second one. That is:
[tex]y=21-x[/tex][tex]\begin{gathered} 4x+6(21-x)=104 \\ 4x+126-6x=104 \\ -2x=104-126 \\ -2x=-22 \\ x=\frac{-22}{-2} \\ x=11 \end{gathered}[/tex]Therefore, the student has taken 11 four credit courses.
What function translates the function f(x) = to the right 2 units and up 10 units?
g(x)= |
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Answer:
g(x) = | x - 2 | + 10
Step-by-step explanation:
given g(x) then g(x± h ) is a horizontal translation of g(x)
• if h > 0 then a move to the left of h units
• if h < 0 then a move to the right of h units
here the move is 2 units to the right, then
g(x) = | x - 2 |
given g(x) then g(x) + c is a vertical translation of g(x)
• if c > 0 then a move up
• if c < 0 then a move down
here the move is 10 units up , then
g(x) = | x - 2 | + 10
Find the volume of the figure. Round your answers to the nearest tenth. It is recommended you use the button on your calculator to solve. 8 mi. 5 mi. Volume of the cylinder = mi3
Answers
Write out the volume of a cylinder shown below
Formula
[tex]\begin{gathered} \text{Volume of a cylinder = }\Pi r^2\text{ h} \\ where\text{ radius = 5mi , height = 8mi , }\Pi\text{ = 3.142} \\ \text{Volume of a cylinder = }3.142x(5)^2x8 \\ V=628.4mi^3 \\ ThereforeVolumeofthecylinder=628.4mi^3\text{ (nearest tenth)} \end{gathered}[/tex]Hence the volume of the figure = 628.4mi³
2. Solve each problem in two different ways as modeled in the example,Example; } x 6 = ?---&*6=zmedena. x 164x 16Kb. x12fx 12
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Let's begin by listing out the given information:
[tex]\begin{gathered} \frac{2}{3}\cdot6=\frac{2\cdot6}{3}=\frac{12}{3}=4 \\ \frac{2}{3}\cdot6=2\cdot\frac{6}{3}=2\cdot2=4 \\ \\ \frac{3}{4}\cdot16=\frac{3\cdot16}{4}=\frac{48}{4}=12 \\ \frac{3}{4}\cdot16=3\cdot\frac{16}{4}=3\cdot4=12 \\ \\ \frac{4}{3}\cdot12=\frac{4\cdot12}{3}=\frac{48}{3}=16 \\ \frac{4}{3}\cdot12=4\cdot\frac{12}{3}=4\cdot4=16 \end{gathered}[/tex]{x+3y=7 -9x+2y=8 elimination or addition method
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The solution to the system of equations is (-10/29, 71/29).
We are given a system of linear equations in two variables.We have two equations and two variables.The first equation is x+3y = 7.The second equation is -9x+2y = 8.We will use the elimination method to solve the equations.x + 3y = 7-9x + 2y = 8Multiply both sides of the first equation by -9.-9x -27y = -63Subtract this newly generated equation from the second equation.(-9x + 2y) - (-9x -27y) = 8 - (-63)-9x + 2y + 9x + 27y = 8 + 6329y = 71y = 71/29Use this value in the first equation to find the value of "x".x + 3y = 7x + 3(71/29) = 7x + 213/29 = 7x = 7 - (213/29)x = -10/29To learn more about equations, visit :
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Which number line
represents the solution to 5+8x < 3(2x+4)
Answers
Answer:
x < 3 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
I cannot see a number line, but the solution can be found by:
5 + 8x < 3(2x+4) Distribute the 3
5 + 8x < 6x + 12 Subtract 6x from both sides
5 + 2x < 12 Subtract 5 from both sides
2x < 7 Divide both sides by 2
x < [tex]\frac{7}{2}[/tex]
or
x < 3[tex]\frac{1}{2}[/tex] This means that all of the numbers less than 3 1/2 are answers.
The quotient of 4 times X and 2 more than Y
Answers
Answer:4x(y+2)
Step-by-step explanation:
Ally bought 4 liters of lemonade, 3,000 milliliters of iced tea, and 2,500 milliliters of fruit punch. How many liters of drinks in total did she buy?
Answers
Answer:
9.5 liters
Explanation:
The volume of each drink that Ally bought is:
• Lemonade: 4 liters
,• Iced tea: 3,000 milliliters
,• Fruit Punch: 2,500 milliliters
Since we are required to find the total in liters, convert the volumes given in milliliters to liters.
[tex]\begin{gathered} 1000\text{ milliliters}=1\text{ liters} \\ \implies1\text{ milliliter}=\frac{1}{1000}\text{ liter} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 3000\text{ milliliter}=\frac{3000}{1000}=3\text{ liter} \\ 2500\text{ m}\imaginaryI\text{ll}\imaginaryI\text{l}\imaginaryI\text{ter}=\frac{2500}{1,000}=2.5\text{ l}\imaginaryI\text{ter} \end{gathered}[/tex]Therefore, the total volume in liters will be:
[tex]4+3+2.5=9.5\text{ liters}[/tex]Ally bought 9.5 liters of drinks in total.
For a particular nature trail, the amounts of time that hikers take to walk the trail are normally distributed.The mean of the times is 30.1 minutes,and the standard deviation is 3.6 minutes.For a sample of 4 hikers,what is the probability that the mean time for the sample is less than 28 minutes?
Answers
Let X be the normally distributed random variable representing the time hiker takes to walk the trail.
Given that mean and standard deviation are 30.1 and 3.6 minutes, respectively,
[tex]\begin{gathered} \mu=30.1 \\ \sigma=3.6 \end{gathered}[/tex]The sample size is 4,
[tex]n=4[/tex]The z-score corresponding to any value of 'x' is given by,
[tex]z=\frac{x-\mu}{\sigma}[/tex]So the probability that the mean time for the sample is less than 28 minutes is calculated as,
[tex]\begin{gathered} P(X<28)=P(z<\frac{28-30.1}{3.6}) \\ P(X<28)=P(z<-0.58) \\ P(X<28)=P(z>0.58) \\ P(X<28)=P(z>0)-P(0From the Standard Normal Distribution Table,[tex]\varnothing(0.58)=0.2190[/tex]Substitute the value,
[tex]\begin{gathered} P(X<28)=0.5-0.2190 \\ P(X<28)=0.281 \\ P(X<28)=28.1\text{ percent} \end{gathered}[/tex]Thus, there is approximately 28.1% probability that the mean time for the sample is less than 28 minutes.
Instruction: State whether the data are symmetrical, skewed to the left, or skewed to the right:a.1; 1; 1; 2; 2; 2; 2; 3; 3; 3; 3; 3; 3; 3; 3; 4; 4; 4; 5; 5b.16; 17; 19; 22; 22; 22; 22; 22; 23c.87; 87; 87; 87; 87; 88; 89; 89; 90; 91
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Based on the data in question a, the graph for the data is skewed to the left. This can be graphed and seen visually but also by calculating the mean and the median of the data set. The mean of the data is 2.85 and the median is 3. Since the mean is less than the median, we can see that the data is negatively skewed, or skewed to the left.
help me pleasee!!
thank you
Answers
Answer:
f(x) = -9 * (x - 2) + 7
f(x) = -9x + 18 + 7
f(x) = -9x + 25
Helps ASAP just 6 and 7 please and thank you
Answers
Using a calculator, we calculate the following
[tex]\begin{gathered} 1.41^2=1.9881 \\ 1.42^2=2.0164 \end{gathered}[/tex]Based on these calculations, the square root of 2 is between 1 and 2.
I need some help with this problem. Thanks.
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Answer:
Natural:G
Whole number: B
Integer: H,D,J
Rational: A,F,E,I
Irrational: C,K
Step-by-step explanation:
What is the degree of a polynomial?
Answers
Answer:
A polynomial's degree is the greatest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial (ignoring the coefficients)
Step-by-step explanation:
The degree of a polynomial is the exponent of the leading term. For example, (x + 1) is a first-degree polynomial because x has an exponent of 1. (x^5 + 2y^4 - 3y^3 + y^2 - x + 3) is a fifth-degree polynomial because x has an exponent of 5.
For right triangle find the missing quantity indicated below express the angle in degrees and minutes not just degrees please and round your answer
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To find the angle we will use the sine theorem, but first we will find the measure of the missing side:
[tex]x^2=1325^2+2569^2[/tex][tex]x=\sqrt[]{1325^2+2569^2}[/tex][tex]x=\sqrt[]{8355386}^{\prime}\text{ }[/tex]measure of angle B must be:
[tex]\frac{sin\text{(B)}}{2569}=\frac{\sin (90^{\circ})}{\sqrt[]{8355386}}[/tex][tex]\sin (B)=\frac{2569}{\sqrt[]{8355386}}[/tex][tex]B=62.72^{\circ}[/tex]Finally convert B to degrees and minutes:
[tex]\frac{1^{\circ}}{60^{\prime}}=\frac{0.72^{\circ}}{m^{\prime}}[/tex][tex]m^{\prime}=0.72\cdot60=43.2^{\prime}[/tex][tex]B=62^{\circ}43.2^{\prime}\text{ }[/tex]The length of a rectangle is 4ft less than 3 times width. Perimeter is 54 ft. What equation can be used to find the width of the rectangle
(3w-4)+2w=54
2(3w-4)+2w=54
w(3w-4)=54
2(4w-3)+2w=54
Answers
Answer:
b
Step-by-step explanation:
Here,
The length of a rectangle is 4ft less than 3 times the width
Then,
length=3w-4ft
Now,
2(l+w)=P
2(3w-4+w)=54
6w-8+2w=54
2(3w-4)+2w=54
Equation b can be used to find the width of the rectangle
Rewrite 0 = 1-2y+14x. As a linear equation
Answers
Answer:
y = 7x + 1/2
Step-by-step explanation:
0 = 1 - 2y + 14x
+2y +2y
2y = 1 + 14x
/2 /2 /2
y = 1/2 + 7x
y = 7x + 1/2
0= 1 - 2y +14x
+2y +2y
