A variable whose value is decided by a random process or experiment is known as a random variable.
Depending on how the experiment or random process turns out, it may have a range of distinct numerical values. Random variables come in two varieties: discrete and continuous. A continuous random variable can take on any value within a specific range, such as real numbers, but a discrete random variable can only take on a countable number of values, such as integers.
This random variable has the following distribution and is discrete in nature:
P(X=0) = probability of red or white = P(red) + P(white)
P(X=1) = probability of green or blue = P(green) + P(blue)
P(X=2) = probability of yellow or violet = P(yellow) + P(violet)
P(X=x) must have a sum of all possible values of 1, which indicates that
P(red) + P(white) + P(green) + P(blue) + P(yellow) + P(violet) = 1
Therefore ,with a probability of 1/3 for each value, this random variable has a discontinuous uniform distribution over the set of values 0, 1, and 2.
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Assume your walking rate is 1. 4 meters per second.
How long would it take you to walk 500 meters?
If the rate of walking is 1. 4 meters per second, then 357.14 sec would take you to walk 500 meters.
We can calculate speed, distance or time using the formula s = d/t, distance equals speed times time. The Speed Distance Time formula can solve for the unknown sdt value given two known values.
Time can be entered or solved in units of seconds (s), minutes (min), hours (hr), or hours and minutes and seconds (hh: mm: ss).
We have,
The rate of walking is 1. 4 meters per second.
The distance to cover is 500 meters.
Now, we know the formula
Speed = Distance/Time
⇒Time = Distance/Speed
⇒Time = 500/1.4
⇒Time = 357.14 sec
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Roberto and Maeko open a pet store and start with 5 hamsters for sale. Hamster populations usually triple every cycle. One cycle is equal to 4 months. Write an equation in function notation to represent the change in the number of hamsters as a function of the cycle number, c. Explain how you determined your equation.
The number of hamsters as a function of the cycle number, c, can be represented by the equation:
f(c) = 5 * 3^c
This equation was determined by the fact that the population triples every cycle and the starting number of hamsters is 5. The function notation is f(c) which represents the number of hamsters as a function of the cycle number. The base of the equation is 3, which represents the rate at which the population triples. The exponent is c, which represents the cycle number. The coefficient is 5, which represents the starting number of hamsters.
HELP ME ASAPPPPP please make it right because i’m in so much trouble rn.
Please only answer problem number 44 from the picture. fill-in-the-blanks using each of the numbers 027 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest. Justify your answer.
By using each of the numbers 0 - 7 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest are,
⇒ 20.3% , 4.56, and 9/1
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Here, We have to use each of the numbers 0 - 7 exactly once.
Hence, The percent, decimal, in fraction below are ordered from least to greatest are,
⇒ 20.3% = 0.203
⇒ 4.56
⇒ 9/1 = 9
Thus, By using each of the numbers 0 - 7 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest are,
⇒ 20.3% , 4.56, and 9/1
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Cynthia buys a shirt for $46 at her favorite store. There is a 7% sales tax on all items in the store. How much tax will she have to pay?
Answer: $3.22 tax
Step-by-step explanation:
7/100 x 46 = $3.22
Answer:3.22$
Step-by-step explanation:3.22$ in the USA
Jackie obtains a 30-year 4/2 ARM at 5% with a 4/7 cap structure in the amount of $313,500. What is the monthly payment during the initial period? (3 points)
$1,832. 69
$1,496. 70
$1,682. 94
$870. 83
The monthly payment during the initial period is about $1,682.94
The type of loan Jackie obtains is an Adjustable Rate Mortgage, ARM, loan, which is a 4/2 ARM
The introductory interest rate of 5% is fixed for the first 4 years, and will be adjusted every 2 years after the first four years.
Let us assume that m represents the initial monthly payment.
[tex]M=\frac{P.(\frac{r}{12} ).(1+\frac{r}{12} )^n}{(1+\frac{r}{12} )^n - 1}[/tex]
where, M is the monthly payment during the initial period
P is the amount on loan
r is the interest rate = 5% = 0.05
n is period = 30 × 12 = 360
Here, P = $313,500
r = 5%
r = 0.05
n = 30 × 12
n = 360
Substituting these values in the above formula we get,
[tex]M=\frac{313500\times (\frac{0.05}{12} ).(1+\frac{0.05}{12} )^{360}}{(1+\frac{0.05}{12} )^{360} - 1}[/tex]
M ≈ 1,682.94
Therefore, the monthly payment is about $1,682.94
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What is the range of this function?
[220, 265]
(220, 265)
(150,275)
[150, 275]
The range of the function is (d) [150, 275]
How to determine the range of the function?The graph that completes the question is added as an attachment
From the graph, we have the following properties:
x values = monthsy values = profitThe range is simply the amount of values between the y axis
In this case represented by the graph, we have:
Minimum y value = 150
Maximum y values = 275
Sinfe both values are inclusive, the range would be [150, 275]
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Find the 9th term of the arithmetic sequence -5x + 2,
-11x - 3,-17x -8,...
Answer: An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. We can call this constant difference "d".
In this sequence, we can see that the difference between consecutive terms is -6x - 5.
The 9th term of an arithmetic sequence can be found by using the formula:
a_n = a_1 + (n-1)d
Where a_n is the nth term of the sequence, a_1 is the first term of the sequence and d is the common difference.
Given the sequence -5x + 2, -11x - 3, -17x -8, ...
The 9th term is:
-5x + 2 + (9-1) (-6x-5) = -5x + 2 - 48x - 40 = -53x -38
Therefore the 9th term of the arithmetic sequence is -53x -38.
Step-by-step explanation:
Rocky has 7 bottles of water. he will buy more bottles of water from the store. the store has 8 cases in stock and each case contains 24 bottles of water. the store will not sell partial cases. the function that models the number of bottles of water rocky will have after his purchase is , where c is the number of cases of water he buys. what is the practical domain of the function?
Answer:
{1, 2, 3, 4, 5, 6, 7, 8}
Step-by-step explanation:
In this problem, we use the variable c to represent the independent quantity. This means that the domain is all possible values for c. Since the store only has 8 cases of water, the domain cannot be any number larger than 8. Since the store only sells complete cases, not partial cases, of water, the domain cannot be a fraction or decimal number. This means that the practical domain, or domain that makes sense for the problem situation, is {1, 2, 3, 4, 5, 6, 7, 8}.
A rectangular piece of metal is 9 in. longer than it is wide, Squares with sides 4 in. long are cut from the four corners, and the flaps are folded upward to form an open box. Which equation indicates that the volume of the box is 56 in.³?
Choose the correct answer below.
OA (x+1)(x-8)=56
OB. x(x +9)(4)=56
OC. (x+1)(x-8)(4)=56
OD. x(x +9)=56
OC (x+1)(x-8)(4)=56 indicates that the volume of the box is 56 in³ because it takes into account the length of the sides after the four corners were cut off, and the height of the box which is 4 in. The equation can be written as (length of sides)(width of sides)(height) = volume.
What is a volume?A volume is a three-dimensional space that contains a specific amount of material, which is commonly measured in liters, cubic meters, or gallons. It is frequently used to calculate the capacity of containers like tanks, bottles, and barrels. Volume may also refer to the quantity of space occupied by an item, such as the volume of a room or the volume of a sphere.
In the given question, OC is the correct answer: (x+1)(x-8)(4)=56. This equation reveals that the volume of the box is 56 [tex]in^{3}[/tex] because it considers the length of the sides after the four corners were taken off, which are (x+1) and (x-8), as well as the height of the box, which is 4 in. The formula is (length of sides)(width of sides)(height) Equals volume. As a result, the equation (x+1)(x-8)(4) = 56 reveals that the box's volume is 56 [tex]in^{3}[/tex].
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The tread of a tire is the part that contacts
the road. Find the surface area of the tread
of a tire with a diameter of 32 inches. Round
your answer to the tenths place.
Answer:
That is correct. The probability of rolling a 2 and a 5 when rolling two dice is 1 in 36, which is considered likely.
Answer:
not enough information
Step-by-step explanation:
The tire is shaped like a cylinder. The tread of a tire is the lateral surface of a cylinder. We know the diameter of the cylinder, 32 inches, but we are not given the width of the tire which is the height of the cylinder, so we cannot calculate the area.
Answer: not enough information
Henry and Jessica skipping rocks across the surface of a pond for every nine rocks at Henry throws he got five of them to skip across the pond for every twelve rocks
Jessica throws she got seven of them to skip across the pond who gets more rocks to skip across the surface of the pond
Jessica gets more rocks to skip across the surface of the pond than Henry.
To determine who gets more rocks to skip across the surface of the pond, we will take the ratio of rocks that skip to rocks that are thrown for each person.
For Henry, the ratio is 5 rocks that skip to 9 rocks thrown i.e 5/9.
For Jessica, the ratio is 7 rocks that skip to 12 rocks thrown i.e 7/12.
Now to compare the ratios, we need to convert them into like fractions. We will do this by making the denominations of both the fractions same.
We will multiply the numerator and denominator of Henry's ratio by 12 to get -
5/9 x 12/12 = 60/108
Also, we will multiply the numerator and denominator of Jessica's ratio by 9 to get -
7/12 x 9/9 = 63/108
Comparing the numerators we get 60<63.
This implies that 60/108 < 63/108.
Therefore, Jessica gets more rocks to skip across the surface of the pond.
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The complete question is -
Henry and Jessica skipping rocks across the surface of a pond. For every nine rocks Henry throws he got five of them to skip across the pond. For every twelve rocks
Jessica throws she got seven of them to skip across the pond. Who gets more rocks to skip across the surface of the pond?
Find the volume of the conical paper cup.
(Radius 3 cm)
(Height 8 cm)
A. 24 cm
O B. 72 7 cm3
C. 64 7 cm3
D. 8 TT cm3
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=8 \end{cases}\implies V=\cfrac{\pi (3)^2(8)}{3}\implies V=24\pi ~cm^3[/tex]
Mr. Grant needs at least 55 paintbrushes for his art classes. He has 25 paintbrushes already and will buy more paintbrushes in packages of 6. Which inequality can be used to find how many packages of paintbrushes, p, Mr. Grant needs to buy in order to have at least 55 paintbrushes?
The packages of paintbrushes, p, that Mr. Grant needs to buy in order to have at least 55 paintbrushes will be at least 5 packages.
How to calculate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
In this case, Grant has 25 paintbrushes already and will buy more paintbrushes in packages of 6.
The inequality to illustrate this will be:
25 + 6p ≥ 55
where P = packages of paintbrushes
Collect the like terms
6p ≥ 55 - 25
6p ≥ 30.
Divide
p ≥ 30 / 6
p ≥ 5
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Paul wants to create a rectangular pig pen using 20 feet of fencing or less. To help determine the possible areas of the pig pen, Paul created a quadratic inequality. A(w) represents the possible total areas in feet2 of the pig pen with respect to width, w, in feet. The graph of the quadratic inequality is shown below:
Which of the following statements could be true about Paul's pig pen?
Select ALL that apply
Paul's pigs will have the maximum possible area if the pen has a width between 3 and 4 feet.
Paul's pig pen has a width of 3 feet and an area of 2 feet2.
With a pen width of 7 feet, Paul could still place 4 pigs in the pen and get them each an average space of approximately 5 feet2.
Paul's pig pen has a width of 2 feet and an area of 16 feet2.
Paul's pig pen h as a width of 16 feet and an area of 8 feet2.
Paul's pig pen has a width of 2 feet and an area of 16 square feet is the true statement.
What is Area of Rectangle?The area of Rectangle is length times of width.
This is a simple calculus problem but it can be solved without calculus, as follows:
let L=length of the pen and W = width
2(L + W) = 20
L + W = 10
L = 10 - W
Let A = area of the pen
A = Length × Width = 10W - W²
Sketch this parabola which has a positive maximum which occurs at W = 10/2
This means the area is maximum when w = 2, in other words the maximum area occurs when the rectangle is a square.
Hence, Paul's pig pen has a width of 2 feet and an area of 16 square feet.
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How do I proof quadrilaterals?
Step-by-step explanation:
1. MN || LO - ( PARALLEL LINES ) .
2. <NMO = <LOM - ( GIVEN ) .
3. <MLO = <ONM - ( REFLEXIVE PROPERTY ) .
4. ..... - ( AAA S-C ) .
A high school class conducts a survey where students are asked about their eye color and whether or not they wear glasses. The two-way table below shows the results of the survey as relative frequencies.
based on the results of the survey, what is the possibility, rounded to the nearest tenth, that a students eye color is brown given that the student wears glasses?
A ) 33.3%
B ) 42.9%
C ) 60.0%
D ) 50.0%
According to the information in the graph, it can be inferred that the percentage of students who have brown eyes among the group that wears glasses is equivalent to 42.9% (option B).
How to calculate the percentage of students who have brown eyes in the group that wears glasses?To calculate the percentage of students who have brown eyes in the group that wears glasses we must perform the following mathematical operation.
We must add all the values of the group that wears glasses
0.04 + 0.08 + 0.12 + 0.04 = 0.280.28 = 100%0.12 = X= 42.85%According to the previous operation, the result must be approximated to 42.9% and the correct option would be B.
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The options for X are:
a. -3
b. 3
c. 0
d. 2/3
[tex]4y-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2}\implies 4\stackrel{y}{\left( -\cfrac{1}{2} \right)}-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2}\implies -2-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( -2-\cfrac{1}{2} \right)=6\left( \cfrac{x}{3}-\cfrac{5}{2} \right)}\implies -12-3=2x-15 \\\\\\ -12-3+15=2x\implies 0=2x\implies \cfrac{0}{2}=x\implies \boxed{0=x}[/tex]
how does the graph of f(x)=2^x+2 compare to the graph of g(x)=2^x +2
Answer: The graph of f(x) = 2^x and g(x) = 2^x +2 are the same.
Explanation: The functions f(x) = 2^x and g(x) = 2^x + 2 are identical. The only difference between them is the constant term in the second function. This constant term does not change the shape, direction or the relative position of the graph of the function, it only shifts the graph along the y-axis. Because both functions have the same base, the graphs will have the same shape, direction and relative position, regardless of the constant term.
Which the correct solution of the equation 1/2a + 2/3b = 50, when b=30
According to the given formula, the value of a is:
60
If b=30 then 1/2a+2/3b=50
How do you find the value of a in the given equation?First, replace the 30 in b.
1/2a+2/3(30)=50
According to the order of operations, we must first multiply 2/3 by 30. yes:
2/3 times 30 is equal to 20.
2/3 times 30/1. 3 is 10 times 30, so 2 times 10 = 20. Now it looks like this:
1/2a+20=50
20 and 50 are similar terms, so I'll put those two together. Move the positive 20 to the other side where the 50 is. 20 has moved to the other side, so it changes sign and becomes negative.
yes:
1/2a=50-20
50-20 = 30
1/2a=30
Multiply each side by 2, because only 2 makes the variable 1a.
1/2a × 2 = 1a
30 times 2 = 60, so:
1a=60, which is also a=60. So a perfect simplification is a= 60
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I need help asap for this
The answer of [tex]\sqrt[4]{125a^{4} }[/tex] is 3.34a. The solution has been obtained by using the concept of exponents.
What is an exponent?
The exponent of a number shows that how many times a particular number has been multiplied by itself. For instance, the number 2^4 means that we are multiplying the number 2 itself by four times. It is enlarged to 2*2*2*2. An exponent is also known as a number's power. One may use a whole number, fraction, negative number, or decimal.
We are given [tex]\sqrt[4]{125a^{4} }[/tex]
This can be also written as (125a^4)^1/4
Splitting the power, we get
⇒[tex]a^{4^{1/4} } 125^{1/4}[/tex]
⇒a 125^0.25
⇒a 3.34
⇒3.34a
Hence, the answer of [tex]\sqrt[4]{125a^{4} }[/tex] is 3.34a.
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Since there are multiple questions so, the question answered above is
[tex]\sqrt[4]{125a^{4} }[/tex]
(8x³ + 6x - 5)/(x + 1)
The quotient for the given expression is 8x^2-8x+14 and the remainder is -19. The solution has been obtained using the method of long division of polynomial.
What is polynomial long division?
A formula for dividing one polynomial by another of the same degree or lower is known as a long division polynomial. Like with long division of numbers, the components of long division of polynomials include the divisor, quotient, dividend, and remainder.
Using Polynomial Long Division,
Dividing : 8x^3 + 6x - 5 ("Dividend")
By : x+1 ("Divisor")
Dividend 8x^3 + 0x^2 + 6x - 5
- divisor * 8x^2 8x^3 + 8x^2
Remainder - 8x^2 + 6x - 5
- divisor * (-8x) - 8x^2 - 8x
Remainder 14x - 5
- divisor * 14 14x + 14
Remainder - 19
Quotient : 8x^2-8x+14
Remainder: -19
Hence, the quotient for the given expression is 8x^2-8x+14 and the remainder is -19.
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What is the perimeter of 6(1/2x + 5)
Answer: The perimeter of a rectangle is the sum of the lengths of all four sides. If one of the sides is 6(1/2x + 5), then we can find the perimeter by multiplying that by 2.
Perimeter = 2*6(1/2x + 5)
Perimeter = 12(1/2x + 5)
To simplify the expression, we can distribute the 12:
Perimeter = 121/2x + 125
Perimeter = 6x + 60
So the perimeter of 6(1/2x + 5) is 6x + 60.
Step-by-step explanation:
Need one last IXL question! Tysm to whoever helps
Answer:
w = 11 , x = 25
Step-by-step explanation:
for Δ ABC ≅ Δ TUV, then corresponding sides must be congruent, that is
AB = TU and BC = UV ( using these to create 2 equations )
- 9x + 20w + 89 = 4w + x + 15 ( subtract 4w + x + 15 from both sides )
- 10x + 16w + 74 = 0 → (1)
and
x + w + 41 = - 18w + 11x ( subtract - 18w + 11x from both sides )
- 10x + 19w + 41 = 0 → (2)
multiplying (2) by - 1 and adding to (1) will eliminate x
10x - 19w - 41 = 0 → (3)
add (1) and (3) term by term to eliminate x
0 - 3w + 33 = 0 ( subtract 33 from both sides )
- 3w = - 33 ( divide both sides by - 3 )
w = 11
substitute w = 11 into either of the 2 equations and solve for x
substituting into (1)
- 10x + 16(11) + 74 = 0
- 10x + 176 + 74 = 0
- 10x + 250 = 0 ( subtract 250 from both sides )
- 10x = - 250 ( divide both sides by - 10 )
x = 25
thus the values x = 25 and w = 11 will make the triangles congruent
You spend $100 on gifts for your family and friends. You buy 40 gifts altogether.
Some gifts were $2 and the rest were $4.
I bought 30 gifts costing $2 each and 10 gifts costing $4 each for my family.
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Let x represent the number of gifts costing $2 and y represent those costing $4
You spend $100 on gifts for your family and friends. Hence:
2x + 4y = 100 (1)
You buy 40 gifts altogether, hence:
x + y = 40 (2)
From both equations:
x = 30, y = 10
A total of 40 gifts was bought
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Find the balance in the account after the given period. $7,700 deposit earning 3.9% compounded monthly, after 4 years.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7700\\ r=rate\to 3.9\%\to \frac{3.9}{100}\dotfill &0.039\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 7700\left(1+\frac{0.039}{12}\right)^{12\cdot 4}\implies A=7700(1.00325)^{48} \implies A \approx 8997.69[/tex]
What percent of the youths surveyed prefer reading electronic books? Round your answer to the nearest tenth of a percent.
Answer: 54% of youths surveyed prefer reading electronic books.
Step-by-step explanation: 74 divided by 100 = 0.74. Divide 40 by 0.74 and you get 54.05%. Round that to 54% and you have your answer.
Kathy and Jake are purchasing a house and are financing $465,000. The mortgage is a 20-year
5/1 ARM at 3. 5% with a 2/7 cap structure. What will the remaining balance be after the first 5 years?
As per the given mortgage, the remaining balance be after the first 5 years is $678125
Here Kathy and Jake are purchasing a house and are financing $465,000. The mortgage is a 20-years 5/1 ARM at 3. 5% with a 2/7 cap structure.
As we know that the formula for the calculation is written as
=> (Mortgage X Rate)/ 12 months
And then we have to subtract the Monthly PI payment from monthly interest on payment.
When we apply the value on it, then we get,
($465,000 x 3.5)/12
= $135625
Then the amount after 5 years is calculated as,
⇒ $135625 x 5
= $678125
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Convert 1.2% to a decimal
Answer: I think its .012
hope this helps
Answer:
0.012
Step-by-step explanation:
HI IM STUCK PLEASE HELP,TEST QUESTION & LIMITED TIME!
Question- Write the standard form equation of a circle given the center of (-7, -15) and an area of A = π. Show all work for your calculations using the equation editor.
The equation of the circle with center (-7, -15) and area π is
(x + 7)² + (y + 15)² = 1.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
We have,
Centre of the circle = (-7, -15)
The equation of a circle is r² = (x - h)² + (y - k)²
Where (h, k) is the center of the circle.
Now,
h = -7
k = -15
The equation of a circle.
r² = (x + 7)² + (y + 15)² _____(1)
Now,
Area = πr²
πr² = π
r² = 1 _____(2)
Now,
From (1) and (2),
(x + 7)² + (y + 15)² = 1
Thus,
The equation of the circle is (x + 7)² + (y + 15)² = 1.
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