The required chances to win the game is more than 50% no matter what two are.
What is probability?The probability is the proportion of the likelihood of an occasion to occur. It estimates the conviction of the occasion. The recipe for likelihood is given by; P(E) = Number of Ideal Results/Number of all out results.
According to question:
Allow the two numbers to be an and b, with a<b. Look at an acknowledgment of X (free of your decision of an or b) with the worth of the main number you see. Assuming that X is greater, switch, in any case keep the number.
The likelihood of winning can be registered as follows:
In the event that you pick a (with 12 possibility), you win assuming you switch, ie if X>a. This has prob. P(X>a).
Comparably assuming you pick b (with 12 possibility), you win on the off chance that you don't switch, ie if X≤b. This has prob. P(X≤b).
So the general likelihood of winning is 1/2+1/2P(a<X≤b), which is marginally bigger than 1/2 in view of our presumptions on X.
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the shipping clerk packs cube with side lengths of 8 inches into a box with side lengths of 10 inches what is the volume of he space left in the larger box for packing materials ?
Answer:
the volume of the space left in the larger box for packing materials is 1000 - 512 = 488 cubic inches.
Step-by-step explanation:
To find the volume of the space left in the larger box for packing materials, we first need to calculate the volume of the smaller cube and then subtract it from the volume of the larger box. The volume of a cube with side length s is given by s^3, so the volume of the smaller cube with side lengths of 8 inches is 8^3 = 512 cubic inches. The volume of the larger box with side lengths of 10 inches is 10^3 = 1000 cubic inches
A lion weighs 7 times as much as a leopard. The combined weight of the cats is 480 pounds. What is the weight of each cat?
Answer:
Leopard: 60 lb
Lion: 420 lb
Step-by-step explanation:
Let x = weight of leopard.
Weight of lion = 7x.
Sum of the weights = x + 7x = 8x
Total weight = 480 lb
8x = 480
x = 60
7x = 7 × 60 = 420
Answer:
Leopard: 60 lb
Lion: 420 lb
Answer: shown below
Step-by-step explanation:
x = 7y
x+y+ 480
7y+y = 480
8y = 480
y = 480/8 = 60 pounds for the leopard
x = 7(60) = 420 pounds for the lion
a. Make a scatter plot and draw a line of fit on a separate sheet of paper.
b. Use the data from 2009 and 2017 to write the equation of the line of fit in slope-intercept form where x is the number of years since 2005.
Explain your process.
a) The scatter plot and the line of fit are given on the second image shown at the end of the answer.
b) The linear function is defined as follows: y = 1.75x + 168.
How to define the linear function?The linear function is defined in the slope-intercept format, as follows:
y = mx + b.
In which:
m is the slope.b is the y-intercept.Considering the data for 2009 and for 2017 from the table, taking x as the number of years since 2005, two points are given as follows:
(4,175) and (12, 189).
The slope, given two points, is calculated as the division of the change in y divided by the change in x, hence:
m = (189 - 175)/(12 - 4) = 14/8 = 1.75.
Hence:
y = 1.75x + b.
When x = 4, y = 175, hence the intercept b is calculated as follows:
175 = 1.75(4) + b
b = 168.
Then the line of fit is:
y = 1.75x + 168.
The scatter plot is composed by all the points of the data-set, considering x as the number of years since 2005, hence:
(0, 169), (2, 175), ... (12, 189).
Missing InformationThe table is given by the first image at the end of the answer.
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There were 425 guests at a hotel. 170 guests ordered food. What percentage of the guests ordered food?
Are closed under addition True or false?
Integers are closed under addition by all the properties. Hence, the answer is True.
Integers are set of zero, positive, and negative numbers. The set of integers is represented by the symbol ‘Z’.
Z= {……-8,-7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,……}
To check if the integers are closed under addition or not we will check out the four properties namely, the closure property, the commutative property, the associative property, and the distributive property.
Let us consider each property one by one -
1. The closure property-
let's take two integers say 5 and 2.
now 5+2=7, but -2+5= -3 which is an integer.
Thus, integers are closed under addition by closure property.
2. The commutative property-
let's take two integers say 5 and 2.
now 5+2=7 and 2+5=-7
hence, we get 2+5 = 5+2.
Thus, integers are closed under addition by commutative property.
3. The associative property-
let's take three integers say 5, 3, and 2.
now (5+3)+2 = 10 and 5+(3+2)= 10
hence, we get (5+3)+2 = 5+(3+2).
Thus, integers are closed under addition by associative property.
4. The distributive property-
let's take three integers say -2, 6, and 5.
now, -2 × ( 6 + 5 ) = -2 × 6 + (-2) × 5 = -12 - 10 = -22
and -2 × ( 6 + 5 ) = -2 × 11 = -22
Hence, -22 = -22
Thus, integers are closed under addition by distributive property.
Hence, we can conclude that integers are closed under addition by all the properties.
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The complete question is-
Are Integers closed under addition. True or false?
How do you find the center and scale factor of a dilation?
Center point of dilation is a fixed point in a plane about which all the points of the figure expanded or contract. And scale factor of a dilation is the ratio of new formed image to the old given image.
Explanation:
Center of a dilation is considered as a fixed point in the given plane.Around the center point of dilation all the points of the given and new figure expanded or contracts.Translate the center of dilation and the given figure , now origin becomes the center and translate back to get the center of dilation.Scale factor can be calculated as the ratio of the dimension of the new image formed to the dimensions of the old given image.If new or old images not defined then ratio of larger to the smaller image gives the scale factor.Therefore, the center of the dilation can be find using the translation and scale factor can be calculated using the ratio of the new to the old images.
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Solve the system of linear equations by graphing. y = –y equals negative StartFraction 5 over 2 EndFraction minus 7.x – 7 x + 2y = 4 What is the solution to the system of linear equations?
x=-9/2 and y=17/4 are the solution to the system of linear equations.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The system of linear equations are:
y=-5/2x-7..(1)
x+2y=4...(2)
x=4-2y
Subtract x value in equation 1.
y=-5/2(4-2y)-7
y=-20/2+5y-7
y=-10+5y-7
y=5y-17
Subtract both sides by 5y
y-5y=-17
-4y=-17
Divide both sides by 4
y=17/4
Now add y value in equation 2.
x+2(17/4)=4
x+17/2-4=0
x+9/2=0
x=-9/2
Hence, x=-9/2 and y=17/4 are the solution to the system of linear equations.
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I dont know this problem(please help)
Inequality (please check the attached image)
Let the number of pens be p and number of pencil cases be c.
Each pen costs php 20 and all pens cost 20p.Each pencil case costs php 40 and all pencil cases cost 40c.Total amount Dona needs to make is at least 2000.Use given information and set inequality:
20p + 40c ≥ 2000Simplify it by dividing all terms by 20:
p + 2c ≥ 100If number of pens is more than 100, we get:
p > 100Substitute this into inequality:
100 + 2c ≥ 100 Subtract 100 from both sides2c ≥ 0 Divide both sides by 2c ≥ 0If Dona sells more than 100 pens then she will exceed php 2000 regardless the number of pencil cases sold.
Latanya has $1.90 worth of nickels and dimes. She has a total of 24 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Latanya has.
The number of nickels and dimes Latanys have is 10 and 14.
What is an equation?An equation is a mathematical statement of two expressions connected by an equal sign.
We have,
Total coins = 24
$1 = 20 nickels
$1 = 10 dimes
Now,
Number of nickels = N
Number of dimes = D
Now,
N + D = 24 ____(1)
N = 24 - D _____(2)
0.05N + 0.1D = 1.90 ____(3)
Putting (2) in (3) we get,
0.05(24 - D) + 0.1D = 1.90
1.2 - 0.05D + 0.1D = 1.90
0.05D = 1.90 - 1.2
0.05D = 0.7
D = 0.7 / 0.05
D = 14
Now,
N = 24 - D
N = 24 - 14
N = 10
Thus,
The number of nickels is 10.
The number of dimes is 14.
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Multiply:
-6 x -10 =??
Answer: 60
6 x 10 is 60 and a negative times a negative is positive.
Answer: 60 hope this helps
Two mountain bikers leave from the same parking lot and head in opposite directions on two different trails. The first rider goes 8 km due East, then rides due south for 15 km. The second rider goes 8 km due West, then changes direction and rides 20 degrees west of due north for 15 km. (See the picture below.) Both riders have been traveling for 23 km, but when they stopped, which one was further away from the parking lot?
When both riders have stopped, the person that is further away from the parking lot is; The second rider.
How to use Pythagoras theorem and law of cosine?Let the required distance be represented by x.
Using Pythagoras theorem, we have:
hypotenuse² = opposite² + adjacent²
x = √(8² + 15²)
x = √289
x = 17 km
This means that the first biker is 17.0 km from the starting point.
Using the law of cosine which is given by the expression;
c² = a² + b² - 2ab cos C
x² = 8² + 15² - 2(8*15) cos (160)
x = 20.22 km
This means that the second biker is 20.22 km from the starting point.
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why might you consider using raw scores for as long as possible before assigning a letter grade to a student
The final scores will be dependent on the prior ones.
What is combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components
raw scores for as long as possible before assigning a letter grade to a student.
Because the final scores will be dependent on the prior ones.
Hence The final scores will be dependent on the prior ones.
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how many nonzero terms of the maclaurin series for ln(1 x) do you need to use to estimate ln(1.4) to within 0.000001?
We need to use 7 terms to estimate the value of ln(1.4) to within 0.0001.
What is the Maclaurin series?A Maclaurin series is a function that is used to estimate the values functions, evaluate the sum, or determine the value of the anti-derivative of a function.
We have:
f(x)=ln(1+x)
Expansion of In(1+x) up to seven terms is:
In(1+x) = x - x^2/2 + x^3/3 - x^4/4 + x^5/5 - x^6/6+ x^7/7
Where it is known that -1 <= x <= 1
Put x=0.4 in the above series:
ln(1.4) = 0.4 - 0.4^2/2 + 0.4^3/3 - 0.4^4/4 + 0.4^5/5 - 0.4^6/6+ 0.4^7/7
We get:
ln(1+4) = 0.3365333
Therefore, we need 7 terms to estimate the value of ln 1.4 to within 0.0001.
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What equation is graphed in this figure?
A: y−4=−13(x+2)
B: y−3=13(x+1)
C: y+2=−3(x−1)
D: y−5=3(x−1)
Answer: D
Step-by-step explanation:
The line is positive and not very steep. For slope, 13 is too steep, -13 and -3 are negative. It must be y-5=3(x-1), which has an accurate slope of 3.
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Question 4
Yellow Taxi service charges a $15 flat fee plus $2.50 per mile traveled. The charges for
Black and White Taxi service are shown in the graph, where x is the number of miles
and y is the total cost.
18
16
14
12
10
8
6
2
O1 2 3 4 5 6 7 8 9 x
Johnny needs to travel 5 miles. How much will it cost Johnny if he pays the least
amount possible?
Part B
How far does Johnny need to travel so that the cost is the same for both taxi services?
miles
9
The least amount possible is $25 and the number of miles is 25 miles
How much will it cost Johnny if he pays the least amount possible?From the question, we have the following parameters that can be used in our computation:
Yellow Taxi service charges a $15 flat fee plus $2.50
This means that
Yellow Taxi: y = 15 + 2.5x
For the graph, we have
y-intercept = 10
(x, y) = (0, 10) and (2, 16)
So, the slope is
slope = (y₂ - y₁)/(x₂ - x₁) = (16 - 10)/(2 - 0) = 3
So, we have
Black and White Taxi service: y = 10 + 3x
Yellow Taxi: y = 15 + 2.5x
When he travels for 5 miles, we have
Black and White Taxi service: y = 10 + 3 * 5 = 25
Yellow Taxi: y = 15 + 2.5 * 5 = 27.5
Hence, the least amount possible is $25
Distance so that the cost is the same for both taxi servicesThis means that we equate the above equations
So, we have
15 + 2.5x = 10 + 3x
Evaluate the like terms
0.5x = 5
Divide
x = 25
Hence, the distance is 25 miles
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what expression is equivalent to
5-(6g-7)+5g
Answer:
-g+12
Step-by-step explanation:
How do you find the coordinates of a dilation?
In order to dilate something on a coordinate plane, multiply the coordinate with the scale factor. This process is known as mapping.
What is a dilation?
Dilation is a process of altering a thing. It is a process of renewal that to make the objects smaller or larger, with the use of specific scale factor.
The new figure that is the result of dilation is known as the image. Initial figure is referred to as the pre-image.
What is a center of dilation?
Center of dilation is the resizing that happens from a point. The objects/figures are expanded or contracted from the center of dilation.
Scale factor is a figure by which the size of any geometrical figure can be resized, with respect to its original size. The scale factor is multiplied to get image.
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Which must be true? line segment a n is-congruent-to line segment l b line segment n c is-congruent-to line segment b z anglebmz is-congruent-to anglecmz anglezbm is-congruent-to anglezcm
The lines or angles with measure must be true for the lines and angles.
To predict the truthfulness of the statements, we must understand the concept of congruency. Any two entities will be congruent if they measure the same. In the question, the line AN will be congruent to line segment LB and line NC will be congruent to line BZ.
Similarly, the angle measurements should also be same to the angles to be congruent. In case of same angles, the Angle BMZ will be congruent to Angle CMZ and Angle ZBM will be congruent to Angle ZCM.
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Answer: D
Step-by-step explanation:
Determine the value of the expression −2(36−8)+(−3).
Answer:-59
Step-by-step explanation:
-2*36 + -2*-8
-72+16-3
-56-3
-59
Give the equation of the circle centered at the origin and passing through the point (12,0)
a rectangular horse pasture is bounded on one side by a stone wall and on the other three sides by a single wire strand of electric fence. using 400 feet of wire, what is the largest area, in square feet, that can be enclosed?
The rectangular horse pasture's largest area, in square feet, can be enclosed in [tex]80000m^{2}[/tex]
Let the sides of the rectangle-shaped fence be a and b.
We have to use wire for the three sides of the fence.
[tex]a+b*2=800[/tex]
Area A is given by
[tex]A=a*b[/tex]
Also, we can write A as a function of b
[tex]A=A(b)\\=(800-2*b)b=800b-2b^{2}[/tex]
Taking the derivative of A
[tex]A'=800-4b\\A'=0\\b=200m[/tex]
Then the length of the other side
[tex]a=800-2*200\\=400m[/tex]
The largest area
[tex]A=400*200\\=80000m^{2}[/tex]
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Isla sells baked good from her home kitchen. She offers decorated cookies for $15 per dozen and cupcakes for $13 per dozen. It takes her an hour to decorate a dozen cookies, but only 20 minutes to decorate a dozen cupcakes. She would like to make at least $300 per week and not put in more than 20 hours of work per week.
A: Create a system of linear inequalities that fits the situation.
B: Isla just discovered that she is running out of cake mix for the cupcakes and royal icing for the cookies. She can make a maximum of 40 dozen cupcakes and 12 dozen cookies. What are the new inequalities you need to add to your problem?
C: What is the maximum amount of baked goods that she could make? (cupcakes, cookies)
D: How much will she earn if she made the maximum amount of baked goods?
E: How long will it take her to make the maximum amount of baked goods? (minutes and hours)
F: What is the least amount of time she could work and still earn $300? What baked goods would she make?
Answer:
A: The system of linear inequalities that fits the situation is:
15x + 13y >= 300
60x + 20y <= 1200
Where x is the number of dozen cookies and y is the number of dozen cupcakes.
B: The new inequalities that need to be added to the problem are:
x <= 12
y <= 40
C: The maximum amount of baked goods that she could make is:
x = 12
y = 40
D: The amount she will earn if she made the maximum amount of baked goods is:
15x + 13y = 15 * 12 + 13 * 40 = $660
E: The time it will take her to make the maximum amount of baked goods is:
60x + 20y = 60 * 12 + 20 * 40 = 960 minutes = 16 hours
F: The least amount of time she could work and still earn $300 is:
15x + 13y = 300
x + y = 20
Solving this system of equations, we get:
x = 8
y = 12
In this case, she would make 8 dozen cookies and 12 dozen cupcakes in a minimum of 8 hours.
Step-by-step explanation:
In a city, there are 16 swimming pools. On weekends, 6 of the pools are open.
George says the ratio of pools open on weekends to the total number of pools is 6:16.
Emma says the ratio of pools open on weekends to the total number of pools is 6:10.
Which student is correct? PLEASE....... Explain.
The student that is correct is George as the ratio of pools open on weekends to the total number of pools is 6:16.
What is the ratio?Ratio is the relationship between two or more numbers. It is the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.
In order to determine the ratio between the number of pools open on the weekend to the total number of pools express the numbers that represent each value as ratios.
This will be:
= number of pools open on weekends: total number of pools
= 6 : 16
George is correct.
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Please help!! Thank you!!
Answer:
The cellular plan allows you to use 4 gigabytes and charges you a flat $90. After 4 gigabytes have been used then, every gigabyte after that is an extra $20.
the area of a rectangle is 105 sq in and the length of one side is 7 in. what is the length of the perimeter?
The length of the perimeter is 44cm if the area of a rectangle is 105sq in and length of one of the side is 7 in.
What is meant by perimeter?A perimeter is a closed path that encompasses, surrounds, or delineates something, whether it be a two-dimensional shape or a one-dimensional length. The outermost border of an ellipse or circle is its circumference.
Knowing the perimeter is helpful in a variety of circumstances. Calculated perimeter refers to the length of fence required to entirely enclose a yard or garden.
Given,
Area of a rectangle=105cm²
And also given that,
Width w=7cm
Area= Length× Width
Length=Area/Width
Length-105/7
Length=15cm
Here, Now we have to calculate the perimeter of a rectangle
Perimeter=2(Width+ Length)
Perimeter=2(7cm+15cm)
Perimeter=44cm.
Hence, the length of the perimeter is 44cm.
Therefore, the length of the perimeter is 44cm if the area of a rectangle is 105sq in and length of one of the side is 7 in.
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A Roth IRA receives $6000 per year. How long would it take to reach $1000000 with an interest rate in a mutual fund of 8% compounded monthly
The time taken to reach $1000000 with an interest rate in a mutual fund of 8% compounded monthly is about 64 years and 2 months.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $6000
r = 8%
n = 12
A = $1000000
Now,
1000000 = 6000 [tex](1 + 0.08/12)^{12t}[/tex]
1000/6 = [tex]1.0067^{12t}[/tex]
log on both sides.
log 166.67 = 12t log 1.0067
2.22 = 12t x 0.0029
12t = 2.22 / 0.0029
12t = 765.52
t = 765.52/12
t = 64.163 years
This means,
About 64 years and 2 months.
Thus,
The time taken to reach $1000000 is 64 years and 2 months.
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Is dilate getting bigger or smaller?
The dilation will change the size of the figure, so it can be getting bigger or smaller
The dilation is the process of changing the size of the figure, but the shape of the figure will be same. Therefore we can say that the dilation is one form of the transformation of the figure
The dilation can be increase the size or decrease the size
If you consider the case of dilation with scale factor, when the scale factor is greater than 1 the size will be bigger and if the scale factor is between 0 and 1 the size will be smaller than original size
Therefore, the dilation can be getting bigger or smaller
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please helppp!!!
Solve for x.
3 1/2≥1.4x
x ≥ 2 1/2
x ≤ 2 1/2
x ≥ 4 9/10
x ≤ 4 9/10
The value of the inequality will be;
⇒ x ≤ 2 1/2
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 3 1/2 ≥ 1.4x
Now,
Since, The inequality is,
⇒ 3 1/2 ≥ 1.4x
Hence, Solve for x as;
⇒ 7/2 ≥ 1.4x
⇒ 3.5 ≥ 1.4x
⇒ 3.5/1.4 ≥ x
⇒ 35/14 ≥ x
⇒ 5/2 ≥ x
⇒ x ≤ 2 1/2
Thus, The value of the inequality for x is;
⇒ x ≤ 2 1/2
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Given a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y. O A. Prediction values are meaningful for all X-values that are realistic in the context of the original data set. O B. Prediction values are meaningful only for x-values that are not included in the original data set. O c. Prediction values are meaningful only for X-values in (or close to the range of the original data.
The values of x that provide meaningful predictions for the output value y are given as follows:
c. Prediction values are meaningful only for X-values in (or close to the range of the original data.
What are regression equations?Regression equations are built from a sample of a data-set, and are used to model the entire data.
Depending on the behavior of the data, the regression equation can be linear, quadratic, logistic, exponential, and so on...
These regression equations are not valid for all values of the input x, some conditions are given as follows:
Values of x that are realistic in the data-set -> time cannot be negative, for example.Values of x that are close to the range of the data-set. -> a linear function from the previous 5 years can preview the measure in 5 years but it is unlikely to be accurate in 100 years.More can be learned about regression equations at https://brainly.com/question/26755306
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