The probability that a person chosen at random uses both internet connections is 1/9
Total number of people = 27
Number of people who use ADSL lines = 16
Number of people who use wireless internet = 15
Number of people who use neither of the two = 3
Let the number of people who use only ADSL lines and wireless internet be denoted by A and B respectively.
Then A + B + A∩B + 3 must be equal to 27
A + B + A∩B = 24
further, we can see that
(A + A∩B) = 16
B + 16 = 24
B = 8
Also, (B + A∩B) = 15
8+ A∩B = 15
A∩B = 7
Thus, the number of people who use both internet connections = 7
Now, P(A∩B) = 7/27
= 1/9
Hence, probability that a person chosen at random uses both internet connections is 1/9.
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Player A finished first in a tournament at a golf club with a score of 8, or eight strokes under par. Tied for 46th place was Player B, with a score of +9, or 9 strokes over par. What was the difference in scores between Player A and Player B?
The difference in scores between Player A and Player B will be 17.
How to illustrate the information?From the information, Player A finished first in a tournament at a golf club with a score of 8, or eight strokes under par. Player B, had a score of +9, or 9 strokes over par.
Therefore, the difference in scores between Player A and Player B will be:
= 9 - (-8)
= 9 + 8
= 17
Therefore, the difference in scores between Player A and Player B will be 17.
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The perimeter of the rectangle below is 166 units. Find the value of y.
4y + 2
Sy
The value of y is 9.
Perimeter is the total length of the boundary of any closed shape. It is basically the sum of all the sides of a given figure.
Perimeter of a rectangle is given by [ 2( l + b ) ] or (2 l + 2 b ) or
( l + l + b + b), here l and b represent the length and breadth of the given rectangle.
Perimeter of the given rectangle = 166 units ( given )
Length of the given rectangle = 5y ( given )
Breadth of the given rectangle = (4y + 2) ( given )
By putting values in the formula, we get
perimeter = 2 ( l + b )
166 = 2 [ (5y) + (4y + 2) ]
166 = 2 [ 5y + 4y + 2 ]
166 = 2 [ 9y + 2 ]
166 = 2*9y + 2*2
166 = 18y + 4
166-4 = 18y ( moving 4 to other side thus changing the sign to negative )
162 = 18y
162/18 = y ( moving 18 to other side for further solution )
y = 9
Therefore, the value of y for which the perimeter of the given rectangle is 166 units is 9.
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The value of y is 9.
The whole length of any closed shape's boundary is known as its perimeter. In essence, it is the total of a given figure's sides.
A rectangle's perimeter can be calculated using [2(l + b)] or (2 l + 2 b) or
(l + l + b + b), where l and b stand for the provided rectangle's length and width
The rectangle's perimeter is 166 units ( given )
The rectangle's length is 5y ( given )
Given rectangle's width equals (4y + 2) ( given )
When we enter values into the formula, we obtain
perimeter = 2 ( l + b )
166 = 2 [ (5y) + (4y + 2) ]
166 = 2 [ 5y + 4y + 2 ]
166 = 2 [ 9y + 2 ]
166 = 2*9y + 2*2
166 = 18y + 4
166-4 = 18y ( moving 4 to other side thus changing the sign to negative )
162 = 18y
162/18 = y ( moving 18 to other side for further solution )
y = 9
Therefore, the value of y for which the perimeter of the given rectangle is 166 units is 9.
Steven has a rope that is 6 ft long. He cuts it into 9 pieces, as shown in the model.
In a survey of 292 professional athletes, it was found that 135 of them owned a convertible, 117 of them owned a giant screen TV, and 136 owned a sporting goods store. 29 owned a convertible and a store, 50 owned a TV and a store, and 57 owned a covertible and a TV. 10 owned all three items.
Using Venn sets, it is found that 30 athletes own none of the items.
What is the missing information?The missing information is the question, which asks how many athletes own none of the items.
What are the Venn Sets?For this problem, we consider the following sets:
Set A: athletes that have a convertible.Set B: athletes that have a giant screen TV.Set C: athletes that owned a sporting goods store.10 owned all three items, hence:
(A ∩ B ∩ C) = 10.
57 owned a convertible and a TV, hence:
(A ∩ B) + (A ∩ B ∩ C) = 57.
(A ∩ B) = 47.
50 owned a TV and a store, hence:
(B ∩ C) + (A ∩ B ∩ C) = 50
(B ∩ C) = 40.
29 owned a convertible and a store, hence:
(A ∩ C) + (A ∩ B ∩ C) = 29.
(A ∩ C) = 19.
136 owned a sporting goods store, hence:
C + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 136
C + 19 + 40 + 10 = 136
C = 67.
117 of them owned a giant screen TV, hence:
B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 117
B + 47 + 40 + 10 = 117
B = 20.
135 of them owned a convertible, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 135
A + 47 + 19 + 10 = 135
A = 59.
There were 292 athletes on the survey, hence the number who owned none is given as follows:
None + A + B + C + (A ∩ B) + (A ∩ C) + (B ∩ C) + (A ∩ B ∩ C) = 292
None + 59 + 20 + 67 + 47 + 19 + 40 + 10 = 292
None + 262 = 292
None = 30.
30 athletes own none of the items.
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Use 3.14 for pie it’s __Units squared
The Area of the figure ≈ 19 units²
What is the Area of a Semicircle and a Triangle?Area of a semicircle = 1/2(πr²), where r is the radius.
Area of a triangle = 1/2(b)(h), where b is the base and h is the height of the triangle.
The figure can be decomposed into a semicircle and a triangle.
Area of the figure = 1/2(πr²) + 1/2(b)(h)
r = 1/2(7) = 3.5 units
π = 3.14
b = 7 units
h = 3 units
Substitute
Area of the figure = 1/2(3.14)(3.5²) + 1/2(7)(3)
Area of the figure ≈ 19 units²
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You have the following information on Zip's Diner, Inc.: sales to working capital = 8 times, profit margin = 5 percent, net income available to common stockholders = $20 million, and current liabilities = $4 million. What is the firm's balance of current assets?
The balance of current assets of the firm is 54 million dollars.
The total of all current assets is the current asset balance. These include cash, cash equivalents, pre-paid expenses, inventories, and any other assets that are anticipated to be turned into cash throughout the course of the following year.
Any debts owed by your business to others, including bank loans, mortgages, unpaid bills, IOUs, and other sums of money, are referred to as liabilities.
We know that to calculate the balance of current assets we use the formula.
Current assets=working capital +current liabilities
Working capital=net income÷(profit margin × sales to working capital)
Now given the working capital=$20 million
Profit margin=5%
Working capital=20÷(8×5%)
or, working capital = 50
Now current assets=Working capital+liabilities
Hence balance of current assets= 50+4 million dollars
=54 million dollars
Therefore the firm's balance of current assets is 54 million dollars.
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Is 1/2 and 9/3 integers, rationals or irrational numbers
XY=3K-2,YZ=7K+4,XZ=4K+38
Answer:
6
Step-by-step explanation:
Due to the segment addition postulate, XY + YZ = XZ.
By substituting the values in, we get that [tex](3k-2)+(7k+4)=4k+38[/tex]
Simplifying gives us that [tex]10k+2=4k+38[/tex]
[tex]6k=36[/tex]
[tex]k=6[/tex]
In a survey 738 of homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was 52.44 with standard deviation 10.98 . Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between 41.46 and 63.42. Round to the nearest whole number
The number of plans that cost between 41.46 and 63.42 is 504 to the nearest whole number
How to solve for the estimation of plansWe have the following data to solve this problem with
n = 738 home owners
standard deviation sd = 10.98
The number of plans is between 41.46 and 63.42
Such that we will have
p(41.46 < x< 63.42)
Then we would have
P(41.46 - 52.44 / 10.98) < z< (63.42 - 52.44 / 10.98)
= P (-1 < z < 1)
We have p(z < 1) = 0.8413
therefore p(z > 1) = 1 - 0.8413
= 0.1587
0.8413 - 0.1587 = 0.6826
This is the same as 68.26%
68.26% x 738 = 503.76
~ 504
Therefore we would have the conclusion that the number of plans that cost between 41.46 and 63.42 is 504 to the nearest whole number.
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Planes A and B intersect.
Which describes the intersection of line m and line n?
point W
point X
point Y
point Z
Answer:
Point W.
Step-by-step explanation:
Line [tex]n[/tex] is on plane [tex]A[/tex]. Line [tex]m[/tex], however, is not on any plane shown, but intersects plane [tex]A[/tex] and line [tex]n[/tex].
If a rectangle has a side that is 8 more than 4 times the length and the perimeter is
166 inches. What are the measures of the sides.
Answer:
2 of the sides are 15 inches and the other 2 sides are 68 inches
Step-by-step explanation:
2(8+4L)+2L=166
16+8L+2L=166
16+10L=166
10L=150
L=15
15(4)+8=68
In a certain federal prison, it is known that 2/3 of the inmates are under 25 years of age. It is also known that 3/5 of the inmates are male and that 5/8 of the inmates are female or 25 years of age or older. What is the probability that a prisoner selected at random from this prison is female and at least 25 years old?
The probability that a prisoner selected at random from this prison is female and at least 25 years old is 1/64
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
GIven that 2/3 of the inmates are under 25 years of age also, that 3/5 of the inmates are male and that 5/8 of the inmates are female or 25 years of age or older.
The number of mother inmates = 75% (100) = 75
The number of inmates, who are not mothers = 100 - 75 = 25
Selecting an inmate who is not a mother = 1/4
Selecting 3 female who are not mothers = 1/64
Therefore, the probability that a prisoner selected at random from this prison is female and at least 25 years old is 1/64
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How many times larger is (1.064 x 101) than (7 x 10−1)?
Answer:
177.464x−1
Step-by-step explanation:
How many times larger is (1.064x⋅101)+(7x⋅10−1)
Remove parentheses.
1.064x⋅101+7x⋅10−1
Simplify each term.
Multiply 101 by 1.064.
107.464x+7x⋅10−1
Multiply 10 by 7.
107.464x+70x−1
Add 107.464x and 70x.
177.464x−1
a parallelogram has an area of 28 square feet and a height of 4 feet what is its base? yall help me please . i really appreciate it. :D
Which of the following are factors of 96? Select ALL that apply.
18
06
04
012
014
Answer:
6, 4 and 12 are factors
Step-by-step explanation:
Divide 96 by each value. If the result is an integer then it is a factor
96 ÷ 18 = 6.333 ← not a factor
96 ÷ 6 = 16 ← factor
96 ÷ 4 = 24 ← factor
96 ÷ 12 = 8 ← factor
96 ÷ 14 = 6.857.. ← not a factor
 Help please with my math
The monthly payment when Jack takes the loan will be B. $319.44
How to calculate the value?From the information, the interest will be:
= Principal × Rate × Time / 100
= ($10000 × 5 × 3)/100
= $1500
The total amount to be repaid will be:
= $10000 + $1500
= $11500
Therefore, the monthly payment will be:
= $11500 / 36
= $319.44
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Approximate -16+√40 to the nearest tenth.
A:9.7
B:6.3
C:-6.3
D:-9.7
Answer:
D. -9.7
Step-by-step explanation:
the square root of 40 is 6.32
-16 + 6.32 = -9.68
-9.68 rounded the nearest tenth is -9.7
GEMDAS
26-6+ (0+3)
26-6 ÷
26- I need help whit this soon as possible
According to the GEMDAS rule the value of the 26-6+ (0+3)*26-6 ÷26- I:
= [tex]96\frac{10}{13}[/tex]
What is The GEMDAS rule ?The GEMDAS rule can be used to summarize or evaluate difficult numerical equations containing several binary operations. Important Information: 1. In a specific simplification, if you have simultaneous multiplication and division, perform the operations sequentially from left to right.
What is the significance of both the Gemdas ,Pemdas rule?If you mess up the order of parenthesis, exponents, multiplications, including addition and subtraction, the PEMDAS rule prevents you from getting the wrong result.
According to the given data:Applying the GEMDAS rule:
26-6+ (0+3)*26-6 ÷26- I
= 26-6+ (0+3)*26-6 ÷26- I
= 26-6+ 78 -6÷ 26-1
= 26-6+78- [tex]\frac{6}{26}[/tex] -1
= 1258/13
= [tex]96\frac{10}{13}[/tex]
According to the GEMDAS rule the value of the 26-6+ (0+3)*26-6 ÷26- I:
= [tex]96\frac{10}{13}[/tex]
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triangles FIM and LAK below are similar, and LA= AK
Multiple choice
Based on the triangle similarity theorem, the length of AK is: A. 9.
How to Determine the Corresponding Side Lengths of Similar Triangles?Based on the triangle similarity theorem, the ratios of the corresponding side lengths of two triangles that are similar to each other are equal and their lengths are proportional to each other.
Given that triangle FIM and triangle LAK are similar triangles, therefore, the ratio is true:
FM/LK = IM/AK
Length of FM = 8 units
Length of LK = 12 units
Length of IM = 6 units
Length of AK = ?
Substitute
8/12 = 6/AK
8(AK) = (6)(12)
8(AK) = 72
Divide both sides by 8
8(AK)/8 = 72/8
AK = 9
AK = LA = 9
LA = 9 units
Therefore, based on the triangle similarity theorem, the length of AK is: A. 9.
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The cost of Jake's cell phone bill is determined by how many megabytes of
data he uses each month, as shown in the graph below.
Jake's Cell Phone Bill
Cost ($)
70
60
50
40
30
20
10
0
5
10
Data Usage (megabytes)
15
Which equation represents the cost of Jake's cell phone bill, y, based on his
data usage in megabytes, x?
The equation that represents the cost of jake's cell phone bill is -
y = 2x + 40 . Option - B is the correct alternative.
We have a graph representing jake's cell phone bill.
We have to write a equation that represents the cost of jake's cell phone bill.
What is the general equation of a straight line ?The general equation of a straight line is given by -
y = mx + c
where -
m → slope of line.
c → y - intercept of line.
According to the question -
The y - intercept of the line is at the coordinates (0, 40). Now, we have to find the slope of this line. Consider the two coordinates -
A(0, 40) and B(10, 60)
Slope of a straight line is given by -
m = y₂ -y₁ / x₂ - x₁
m = 60 - 40 / 10 - 0
m = 20 / 10
m = 2
Now, substituting the values in the general equation of line, we get -
y = 2x + 40
Hence, Option B → y = 2x + 40 is the correct alternative.
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Which equation matches the graph of the greatest integer function given
below?
The correct is option B. y = [x] + 3; for the given graph of the greatest integer function.
What is defined as the greatest integer function?The greatest integer function returns the largest integer that is less than or equal to x; x represents this function.The greatest integer function is one that returns an integer that is closer to the given real number. It is also known as the step function. This function will return the nearest integer to the given number.Let g(x) be the given graph's function.
The parent function for which is,
f(x) = [x]
In which case, f(x) = 0 in the range [0, 1].
However, according to the graph,
g(x) = 3 in the interval [0,1].
F(x) is moved vertically upward.
→ g(x) = f(x) + 3
→ g(x) = [x] + 3
Thus, the graph for greatest integer function if for equation: y = [x] + 3.
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3. Mrs. Quinto is comparing the Calories in different types of bread. Wheat bread has 150 Calories for every 2 slices. The Calories in two other types of bread are shown in the table and graph. Which bread has the greatest ratio of Calories to slices?
options:
2 - 160
4 - 320
6 - 480 . (white bread)
Rye bread is 0 to 500 .
The bread that has the greatest ratio of Calories to slices is the Wheat bread
How to determine the bread that has the greatest ratio of Calories to slices?The table of values is given as
Wheat bread
Slice - Calories
2 - 160
4 - 320
6 - 480
The missing graph that represents the graph of rye bread is added as an attachment
On the graph, we have the following table of values
Rye bread
Slice - Calories
2 - 130
4 - 260
6 - 390
We start by calculating the rates of each table using
Rate = Calories/Slice
So, we have
Wheat bread = 160/2
Wheat bread = 80
Rye bread = 130/2
Rye bread = 65
80 is greater than 65
Hence, the bread that has the greatest ratio of Calories to slices is the Wheat bread
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y cubed plus 11 y to the power of 4 plus 10 y squared plus y to the power of 4 plus 6 y cubed
The simplified form of the given expression is [tex]10y^{2}+7y^{3}+12y^{4}[/tex].
The given expression is [tex]y^{3}+11y^{4}+10y^{2}+y^{4}+6y^{3}[/tex].
We need to simplify the given expression.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
To simplify any algebraic expression, the following are the basic rules and steps:
Remove any grouping symbol such as brackets and parentheses by multiplying factors.Use the exponent rule to remove grouping if the terms are containing exponents.Combine the like terms by addition or subtraction.Combine the constants.Now, [tex]y^{3}+11y^{4}+10y^{2}+y^{4}+6y^{3}[/tex]
= [tex]10y^{2}+7y^{3}+12y^{4}[/tex]
Therefore, the simplified form of the given expression is [tex]10y^{2}+7y^{3}+12y^{4}[/tex].
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Determine what type of functions the following are and explain how you know:
1. f(x) = 3^(-2x)
2. f(x) = 3x^2
(The options are quadratic or exponential function)
Answer:
1. exponential
2. quadratic
Step-by-step explanation:
2. because the variable has the power two and such functions are regarded as quadratic functions
Using your answer in number two what is 60% of 800
Students
Answer:
480
Step-by-step explanation:
first convert 60% into a decimal which is 0.6, then 800 x 0.6 which you would get 480.
Willa receives a commission of $1,020 for selling a car. If the commission is 5% of the selling price, what is the selling price of the car?
Willa receives a commission of $1,020 for selling a car. If the commission is 5% of the selling price, what is the selling price of the car?
The selling price of the car is [tex]\[/tex]20400.
Given that,
Willa receives a commission of $1,020 for selling a car.
If the commission is 5% of the selling price.
What is the selling price of the car?
Let us take selling price of the car= x
We can write selling price of the car as
$1,020 =5%x
1020=[tex]\frac{x}{20}[/tex]
[tex]x=1020\times20[/tex]
[tex]x=20400[/tex].
Therefore, The selling price of the car is [tex]\[/tex]20400.
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Find the sum of the first 8 terms of the
following series, to the nearest integer.
48, 60, 75
Answer:
952.32
Step-by-step explanation:
Suppose you would like to deliver 20.6 terabytes data from Kansas City to Los Angeles. You have available a 1 Gbps dedicated link for data transfer. Would you prefer to transmit the data via this link or instead use USPS delivery knowing it will take them 2 days to complete the task? Explain.
Using proportions, it is found that the dedicated link would take 5.72 hours, which is significantly less time than the USPS delivery, hence the link should be used.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Each TB has 1000 GB, hence:
20.6 terabytes = 20,600 Gigabytes.
You have available a 1 Gbps dedicated link for data transfer, hence the time it would take for the transfer through the dedicated link is:
20,600/1 = 20,600 seconds.
Each hour has 3600 seconds, hence the time in hours is:
20600/3600 = 5.72 hours.
The dedicated link would take 5.72 hours, which is significantly less time than the USPS delivery, hence the link should be used.
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How do I solve this problem?
The algebraic solution for the variable x is as follows:
x = 9 / 2. How to find the variable x in the equation?The equation is represented as follows;
2 / 5 (2 - x) = - 1 / 3 x + 1 / 2
open the bracket on the left side
2 / 5 (2 - x) = - 1 / 3 x + 1 / 2
4 / 5 - 2x / 5 = - 1 / 3 x + 1 / 2
Add 1 /3 x to both sides
4 / 5 - 2x / 5 = - 1 / 3 x + 1 / 2
4 / 5 - 2x / 5 + 1 / 3 x = - 1 / 3 x + 1 / 3 x + 1 / 2
4 / 5 + 1 / 3 x - 2 / 5 x = 1 / 2
4 / 5 + 5x - 6x / 15 = 1 / 2
4 / 5 - x / 15 = 1 / 2
subtract 4 / 5 from both sides
4 / 5 - 4 / 5 - x / 15 = 1 / 2 - 4 / 5
- x / 15 = 5 - 8 / 10
- x / 15 = - 3 / 10
cross multiply
- x / 15 = - 3 / 10
-10x = - 45
divide both sides by -10
x = 45 /10
x = 9 / 2
Therefore, the algebraic solution for the variable x is 9 / 2.
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In an experiment D and T are both measured correct to 2 significant figures. When D = 8.5 and T = 0.32. Find the lower bound of S. Write the result to 3 decimal places.
The lower bound of S is 26.412 .
Lower bound: The value below each element in the dataset. Upper bound: The value greater than or equal to each element in the dataset. Upper and lower bounds are the maximum and minimum values a number could have before it was rounded. They are also called precision limits. Upper and lower bounds can be written in terms of error intervalsIt is given that D = 8.5 and T = 0.32 and a relation between S and D which is given by [tex]S=\frac{D}{T}[/tex] . Putting value of D and T we get
[tex]S=\frac{8.5}{0.32} \\\\S=26.562[/tex]
The place value of the degree of accuracy is 0.3.
Divide this place value by 2 , we get
[tex]\frac{0.3}{2} =0.15[/tex]
To find the lower bound , we will subtract this amount from the given value , we get
[tex]26.562-0.15=26.412[/tex]
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The complete question mention below :
S=D/T
In an experiment D and T are both measured correct to 2 significant figures.
When D= 8.5 and T=0.32, find the lower bound for S.Write the result to 3 decimal places.
