Answers
Answer: The probability is 3 out of 20
Step-by-step explanation:
Related Questions
Find the values of the variables. Then find the side length of the square 
Answers
Answer:
x = 4y = 8side length = 4Step-by-step explanation:
You have a square with sides labeled (y-4), (3x-8), (2y-12), and you want to know the values of the variables as well as the side length.
SetupAll sides of the square are the same length. Equating two different y-expressions, we get ...
y -4 = 2y -12
We can use the solution to that to find x:
y -4 = 3x -8
SolutionAdding 12-y to the first of these equations gives us ...
8 = y
Using this value in the second equation, we have ...
8 -4 = 3x -8
12 = 3x . . . . . . add 8
4 = x . . . . . . . . divide by 3
The side length is ...
y -4 = 8 -4 = 4
The values of the variables are x = 4, y = 8, and the side length of the square is 4.
Which table represents an exponential function of the form y = b when 0
Answers
Second table represents an exponential function of the form y = b when 0
Define exponential function.A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered. In addition to many other applications, exponential functions are used to estimate populations, carbon date artefacts, assist coroners in determining the time of death, compute investments, and many more. Three of the most popular applications—population expansion, exponential decay, and compound interest—will be covered in this session.
Given,
Second table represents an exponential function of the form y = b when 0
Function: y = bˣ
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you are constructing a cardboard box from a piece of cardboard with the dimensions 4 m by 8 m. you then cut equal-size squares from each corner so you may fold the edges. what are the dimensions (in m) of the box with the largest volume?
Answers
The dimensions (in m) of the cardboard box with the largest volume is obtained as 2 m length.
Define the term largest volume?Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc. Volume is sometimes referred to as capacity.Dimensions of piece of cardboard;
Length = 8 mWidth = 4 m.Let the corner cut length be 'x',
New dimensions;
Length = 8 - 2x Width = 4 - 2xHeight = xVolume = length x width x height
Put the values;
V = ( 8 - 2x ) (4 - 2x) x
Find the solution of the obtained quadratic equation by quadratic formula.
x = 0, 2 and 4.
As, x ≠ 0 and 4.
Thus, x = 2.
Thus, the dimensions (in m) of the box with the largest volume is obtained as 2 m length.
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Simplify. (4i+1)^2
show all work
Answers
(4i+1)² can be simplified to 8i-15
What is Complex number?A complex number is a number of the form a + bi, where a and b are real numbers
Given expression is (4i+1)²
four times of i plus one whole square.
(4i+1)² can be expanded by using algebraic identity
(a+b)²=a²+b²+2ab
(4i+1)²
Now put a as 4i and b as 1
(4i+1)²=16i²+1+2(4i)(1)
Where i²=-1
=-16+1+8i
=8i-15
Hence (4i+1)² can be simplified to 8i-15
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What was the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64
Answers
the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64 was $ 68.73
We have the insurance coverage amount for men of 30 years and for women of 50 years. Therefore, to find the percentage that represents the cost of coverage of the 50-year-old woman based on the cost of coverage of the man, we need to perform the following operation:
Xw= Cw/Cm * 100%
Where:
Cw: cost of coverage for a woman of 50 years.
Cm: coverage cost for a 30-year-old man.
Xw= 819.73/1192.64 *100%
= 68.73
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What is the sum of all the even numbers between 105 and 351?
What is the difference between the sum of all the even numbers between 305 and
609 and the sum of all the odd numbers between 304 and 608?
Answers
The sum of even numbers between 105 and 351 is 28,044 .
What is arithmetic progression ?An additive or arithmetic sequence is a sequence of numbers such that the difference between consecutive terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15 ... is an exponent plus the common difference of 2.
Calculationeven numbers between 105 and 351
the series will start like
106 , 108 , 110 , .................................. , 346 , 348 , 350
this is a arithmetic progression
a = 106 d = 2 l = 350
we need to find n
350 = 106 + ( n - 1 ) 2
350 - 106 = (n -1 ) 2
244/2 = n -1
n = 123
now sum = 123/2 ( 106 + 350)
= 28,044
so the sum of even numbers between 105 and 351 is 28,044 .
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Study each equation, then solve.
8) 5 + r = 6 - r
9) z - 16 = - 16
10) 7n - 7 = 0
Answers
The solution for r in equation 5 + r = 6 - r, r =1/2
The solution for z in equation z - 16 = - 16, z= 0
The solution for n in equation 7n - 7 = 0 , n= 1
(8) 5 + r = 6 - r
Step 1: Rearrange the equation by collecting the like terms
r +r=6-5
Step 2: Simplify r +r=6-5
2r = 1
Step 3: Divide both sides by 2
2r/ 2 =1/2
r =1/2
9) z - 16 = - 16
Step 1; Add 16 to both sides
z-16 +16 = -16 +16
z= 0
10) 7n - 7 = 0
To solve for n
Step 1: Add 7 to both sides
7n - 7 +7 = 0+7
7n =7
Step 2: Divide both side by 7
7n/7 =7/7
n= 1
Therefore, the solution for r in equation 5 + r = 6 - r, r =1/2
The solution for z in equation z - 16 = - 16, z= 0
The solution for n in equation 7n - 7 = 0, n= 1
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Point G is the centroid of right triangle ABC with hypotenuse AB=18in. Find CG.
Answers
Since Point G is the centroid of right triangle ABC with hypotenuse AB=18in. Then CG is 6 in.
What guidelines govern a right triangle?The area of the square whose side is the hypotenuse (the side across from the right angle) in any right triangle equals the sum of the areas of the squares whose sides are the two legs, according to the Pythagorean theorem.
Note that from the question, A triangle's centroid, G, is located 2/3 of the way down one of its medians. We tend must determine the median C's length in order to find CG.
We require the use of Thale's Theorem to get the median length at C. According to this, a right triangle ABC can be encircled by a semicircle with the hypotenuse acting as the diameter.
Therefore, the median C is a point on the semicircle that connects to the diameter of the hypotenuse AB. Since it is connected to the center, median C is a radius. Half of its length, or 18/2, or 9 inches, makes it.
So:
CG is 2/3 down the median, which is:
9 x 2/3 = 6 inches.
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A mixture of 13% disinfectant solution is to be made from 11% and 17% disinfectant solutions. How much
of each solution should be used if 12 gallons of the 13% solution are needed?
There needs to be
gallons of 11% solution and
gallons of 17% solution.
Answers
The mixture of 13% disinfectant solution needs to be made with 8 gallons of 11% solution and 4 gallons of 17% solution respectively.
How to find the number of gallons of solution needed?Let
gallons of 11% solution = xgallons of 17% solution = yx + y = 12
0.11x + 0.17y = 0.13 × 12
x + y = 12
0.11x + 0.17y = 1.56
From (1)
x = 12 - y
Substitute into (2)
0.11x + 0.17y = 1.56
0.11(12 - y) + 0.17y = 1.56
1.32 - 0.11y + 0.17y = 1.56
- 0.11y + 0.17y = 1.56 - 1.32
0.06y = 0.24
divide both sides by 0.06
y = 0.24/0.06
y = 4
Substitute y = 4 into (1)x + y = 12
x + 4 = 12
x = 12 - 4
x = 8
So therefore, the gallons of 11% solution and
gallons of 17% solution needed are 8 and 4 gallons respectively.
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a wooden artifact from an ancient tomb contains 25 percent of the carbon-14 that is present in living trees. how long ago, to the nearest year, was the artifact made? (the half-life of carbon-14 is 5730 years.)
Answers
The artifact was created 11,460 years ago.
Given
that,25% of the carbon-14 found in living trees can be found in a wooden artifact from an ancient tomb and the half-life of carbon-14 is 5730 years Half Time [tex]t_{1/2}[/tex] = 5730 yearsln 2 / k = 5730k = 5730 / ln 2Let Po = 100P(t) =25 after t yearsP(t) = Po e^ -kt25 = 100 e ^ -(5730t / ln 2)5730t / ln 2 = ln 4
By applying
we get,t = 5730 * log⁴₂t = 11460 years Hence, the artifact was made 11,460 years ago.
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(25x^2+4-30x)-(9x^2+4-12x)
Answers
Answer:
16x² - 18x
Step-by-step explanation:
(25x² + 4 - 30x) - (9x² + 4 - 12x) ← distribute this parenthesis by - 1
= 25x² + 4 - 30x - 9x² - 4 + 12x ← collect like terms
= (25x² - 9x²) + (4 - 4) + (- 30x + 12x)
= 16x² + 0 + (- 18x)
= 16x² - 18x
25x^2+4-30x-9x^2+4(-1)-12x(-1)
Simplify:
25x^2-9x^2+4-4-30x+12x
Answer:
16x^2-18x
A quadratic function f has a vertex at (6, −2).
a. Explain what it means for a function to have a vertex at this point.
b. How can you determine if this vertex is a maximum or minimum? Explain.
c. Explain how the values of f(2) and f(10) compare to the value of ƒ (6).
d. Compare the values f(2) and f(10).
Answers
Considering the vertex of the quadratic function at point (6,-2), it is found that:
a) The meaning is that the turning point of the function is at point (6,-2).
b) If the parabola is concave down, then the vertex is a maximum. If the parabola is concave up, then it is a minimum.
c) If the parabola is concave down, then f(2) = f(10) < f(6). If the parabola is concave up, then f(2) = f(10) > f(6).
d) f(2) = f(10).
What is the vertex of a quadratic equation?A quadratic equation is defined by the rule presented as follows:
y = ax² + bx + c.
The vertex can represent either a maximum point or a minimum point, depending on the coefficient a, as follows:
Maximum: a < 0. -> concave down parabola.Minimum: a > 0. -> concave up parabola.The vertex is also the turning point of the graph of the parabola.
In this problem, the coordinates of the vertex are (6,-2), hence:
If the parabola is concave down, all the values are lesser than f(6).If the parabola is concave up, all the values are greater than f(6).When two points are equidistant from the vertex, they have the same numeric value, hence:
f(2) = f(6).
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what is 382 3/10 minus 191 87/100
Answers
Answer:
190 43/100
Step-by-step explanation:
First, you turn the mixed fractions into improper fractions. 382 3/10 is 3823/10, and 191 87/100 is 19187/100. Then, you need to have a common denominator in order to subtract. This turns 3823/10 into 38230/100. 38230/100 - 9187/100 is 19043/100 since you only subtract the numerators. Finally, you turn it back into a mixed fraction by dividing 19043/100. This equals 190 with a remainder of 43. In conclusion, the answer is 190 43/100. I attached the image where I worked it out to show my thought process a bit more as well. I hope this helped! :D
g with normalcdf if 15% of adults in a certain country work from home, what is the probability that fewer than 60 out of a random sample of 500 adults will work from home?
Answers
The probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03
In the given probability case we have;
What is the likelihood that, out of a random sample of 500 persons, fewer than 60 will work from home if 15% of adults in a particular country do so?
Let,
P = 15% = 0.15
n = 500
By considering the binomial distribution case the formula is given by
P( X = x ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ
P( X ≤ 60 ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ
= ⁶⁰∑ₓ=₀ (⁵⁰⁰Cₓ) (0.15)ˣ (1 - 0.15)⁵⁰⁰⁻ˣ
= 0.031
≅ 0.03
Hence, the probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03
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Write the equation of the circle in standard form that has the following: Center (-5,7) and Radius = 4
Answers
Answer:
[tex](x+5)^{2}+(y-7)^{2} =16[/tex]
Step-by-step explanation:
The Standard Form of Circle Equation whose Center is at ( h , k) and Radius of r is given by
[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]
So for our Question
we have ( h , k ) = ( -5 , 7 ) and r = 4
By substitution
[tex](x-(-5))^{2}+(y-7)^{2} =4^{2}[/tex]
Simplify [tex](x+5)^{2}+(y-7)^{2} =16[/tex]
A store manager instructs some new trainees that a barbecue grill priced at $700 winds up costing a customer $714 once the sales tax is included. What is the sales tax percentage?
Write your answer using a percent sign (%).
Answers
Answer:
0.02 or 2%
Step-by-step explanation:
$700(x)=$714
$700(0.02)=14
700+14=714
Peggy is planting a garden. The garden is 103 feet wide by 7 feet long. What is the area of the garden?
Answers
Answer: 721 ft
Step-by-step explanation:
formula for area is a=l*w
Given: w=103, length=7
103*7=721
Answer: The answer 721. When you are finding an area of something you must multiply the length and the width so the information given.
103 x 7 = 721 feet long
Here is the real problem:
It's sloppy as long as you understand the concept : )
PLEASE HELP ITS DUE IN 20 MINUTES
Answers
Answer/Step-by-step explanation:
[tex]-\frac{8}{27} a^{15} = (-\frac{2}{3})^{3} * (a^3)^5 = (-\frac{2}{3} a^{5})^3[/tex]
I hope this helps!
graph each function for the given domain 2x-y=3; d: (-2,0,1,3)
Answers
The range values for the domain of the functions are as follows
x y
-2 7
0 3
1 1
3 -3
How to complete the tables for the graphThe domain are the input values of the graph the output values are solved using the given functions
The given function 2x-y=3
rearranging gives
y = 3 - 2x
solving for the range values using the domain values: (-2,0,1,3)
= 3 - 2x = 3 - 2 * -2 = 7
= 3 - 2 * 0 = 3
= 3 - 2 * 1 = 1
= 3 - 2 * 3 = -3
The graph is attached
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Roscoe is a professional groomer.
What is the unit rate for grooming per hour?
5 dogs per hour
15 dogs per hour
3 dogs per hour
1 dog per hour
Answers
You need to divide the 15 dogs by the 3 hours to get your one hour.
PLEASE HELP FAST!!!! ILL GIVE BRAINLIEST!!!!
A linear function contains the following points.
What are the slope and y-intercept of this function?
A. The slope is 11/2
The y-intercept is (0, -5).
B. The slope is 2/11
The y-intercept is (0, -5).
C. The slope is 11/2
The y-intercept is (-5, 0).
D. The slope is 11.
The y-intercept is (0, -5).
Answers
you are vacationing in jamaica from the united states and have 50 u.s. dollars to spend on souvenirs. how many souvenirs can you buy if each one costs 500 jamaican dollars? (1 u.s. dollar
Answers
The exchange rate if each souvenir costs 200 Jamaican dollars, 38 might be purchased.
The exchange rate refers to the value of one country currency about's currency. It is determined by the foreign currency market, often known as the FOREX market.
Amount needed for vacation = $50 USD = $7,740 JMD
Each souvenir is priced at 200 Jamaican dollars.
One US dollar = 154.8 Jamaican dollars when converted to Jamaican currencies.
50 US dollars = 154.8 × 50
= 7,740 Jamaican dollars
Number of souvenirs you can buy = Amount of money with you for vacation ÷ Cost of each souvenir
= 7,740 Jamaican dollars ÷ 200 Jamaican dollars
= 38.7 souvenirs.
As a result, for 200 Jamaican dollars for each souvenir, about 38 souvenirs may be obtained with 50 US dollars.
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The cost of mailing a package is proportional to the weight of the package. The proportional relationship can be represented with the equation c = 0.8w, where c represents the total cost and w represents weight in ounces. A graph for the equation is shown. graph with x axis labeled weight in ounces and y axis labeled cost in dollars, with a line from 0 comma 0 going through 2 comma 1.6 Which of the following statements is true about the graph shown?
Answers
The correct statement regarding the proportional relationship c = 0.8w is given as follows:
The equation c = 0.8w is correctly represented by the graph.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.
When the two variables x and y are direct proportional, the output variable y is obtained as the multiplication of the input variable x by the constant of proportionality k, as follows:
y = kx.
In this problem, the equation is given as follows:
c = 0.8w.
In which:
c is the cost in dollars -> output -> y-axis of the graph.w is the weight in ounces -> input -> x-axis of the graph.For a input of 2, the output is given as follows:
c = 0.8 x 2 = 1.6.
Hence point (1,0.8) is in the graph, along with point (2,1.6).
Missing InformationThe statements are given as follows:
The equation c = 0.8w is correctly represented by the graph.The graph is incorrect and the line should go through the point (0.8, 1).The x-axis and y-axis are labeled incorrectly.The graph does not show a proportional relationship.More can be learned about proportional relationships at https://brainly.com/question/10424180
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(x+2)(x+3)(x+4) can be written in the form [tex]x^{3}[/tex] + a[tex]x^{2}[/tex] + bx c where a, b and c are positive integers.
Work out the values of a, b and c.
a = (Answer here) (1)
b = (Answer here) (1)
c = (Answer here) (1)
Answers
Answer:
a = 9 ; b = 26 ; c = 24
Step-by-step explanation:
(x^2+3x+2x+6)(x+4)
(x^2+5x+6)(x+4)
x^3+5x^2+6x+4x^2+20x+24
x^3+9x^2+26x+24
pLS HURRY!!!This area model shows the quotient of 1/5+4
What is the quotient?
Enter your answer as a fraction in simplest from by
filling in the boxes.
Answers
The quotient of the fraction is 0.05 and the fraction in its simplest form is 1/20
How find the quotient of a fraction?The quotient of a fraction is the whole number that is obtained when you simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction
Given: 1/5÷4
1/5÷4 = 1/5 × 1/4 (Note: If ÷ change to ×, 4 will change to 1/4 )
= 1/20 = 0.05
Therefore, the quotient of the fraction is 0.05 and 1/20 should be filled in the box
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Enter the equation of the graph in vertex form?
Answers
The equation of the given graph is y = (x + 4)² -5.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
The vertex form of a parabola is y = (x - h)² + k which is opened upward direction and vertex is (h, k).
From the graph, the vertex of the quadratic equation is (-4, -5)
Thus h = -4 and k = -5.
Putting h = -4 and k = -5 in y = (x - h)² + k
y = (x - (-4))² + (-5)
y = (x + 4)² -5
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Redondea 5.2 al número entero más cercano
Answers
The nearest whole number to the number 5.2 is 5.
Given number:
= 5.2
we can determine the whole number of any decimals using the properties that is,
if decimal part < .5 its nearest whole number is 0.
example = 0.5 whole number is 0.
if decimal part > 0.5 its nearest whole number is 1.
In this case,
= 5.2
decimal part = 0.2 < 0
so the nearest whole number is 5.
Therefore the nearest whole number to the number 5.2 is 5.
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What is 150 rounded to the nearest 10th divided by 4
Answers
The value of 150/4 to the nearest tenth is 37.50
What are fractions?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. . In a proper fraction, the numerator is less than the denominator. In improper fraction, the denominator is smaller to the numerator.
The value of 150/4 = 75/2= 37 1/2
1/2 in decimal is 0.5
Therefore 150/4= 37+ 0.5= 37.5
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The equation x=-2 is graphed on the coordinate plane shown.
What is the equation of the line perpendicular to x=-2 that passes through (-9,3)?
What is the parallel line and what is the perpendicular line.
Answers
We will see that the linear equations are:
Parallel line: x = -9
Perpendicular line: y = 3
How to get the parallel and perpendicular lines?Here we have the vertical line:
x = -2
A parallel line to this one will also be vertical, of the form:
x = a
And a perpendicular line to this one will be horizontal, of the form:
y = b
We want the parallel line to pass through (-9, 3)
So our line x = a needs to pass through that point, then:
x = -9
Is the parallel line.
And if the perpendicular line y = b needs to pass through that point, then:
y = 3
Is the perpendicular line.
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A certain airline charges a service fee of 7% for each plane ticket purchased. What is the total price the airline charges for a $320 plane ticket?
Answers
Answer: $342.40
Step-by-step explanation:
There are two ways you can solve this problem:
Simply turning the percentage to a decimal and multiplying it to the $320.
In the picture provided the method at the top represents you multiplying $320 x .07, You might be wondering “why .07 instead of 7%?” Well, if you were turning this number from a percent to a decimal you would shift the decimal point over to the left 2 times.
And so multiplying $320 x .07 = 22.4 or 22.40. Either way works but without the zero is the way you should write it. And you would add 22.4 to $320 and get $342.40.
Also in the picture provided I used the method of proportions.
Where the total is $320 in this case which you would put next to 100% as 100% means complete or the total. And you would put 7% above 100%. Then, proceed to cross multiply $320 by 7 and it will give you, 2240. Then, you divide it by 100. When you divide it you get 22.40. Then you would add it to $320 and get 342.40.