3. (2 marks) A real estate agent has 8 keycards to open new model homes. Only one keycard will open any specific model home. If 40% of these homes are usually left unlocked, what is the probability that the real estate agent can get into a specific home if the agent chooses 3 keycards at random before leaving the office
Answers
Answer:
0.625
Step-by-step explanation:
We are told that the agent has 8 keycards.
We are also told that only one of the keycards can open each home.
Now, if the agent took 3 out of the 8 keycards with him, it means that;
Probability of opening by the keycards = ⅜
We are told that 40% or 0.4 of these homes were left unlocked.
This means that 60% or 0.6 are those that will require a key card.
Thus, probability of agent getting into a specific home is;
P(agent getting into a specific home) = 0.4 + 0.6(⅜)
P(agent getting into a specific home) = 0.4 + 0.6(0.375) = 0.625
Related Questions
If four out of ten people vote. Then in a town with 210,000 people, how many people will not vote?
Answers
!!!/!!.
helppp meeeeeeeeeeee
Answers
Answer:
1st choice
Step-by-step explanation:
$8.75 for each bag which means 8.75x
plus a fee of $18.50 which means + 18.50
.6(2x +4.5y) -.3y = m(x+ny) solve for n
Answers
Answer:
n=0.2(6x+12y-5mx)/my
Step-by-step explanation:
Daniel invests £2200 into his bank account.
He receives 5% per year simple interest.
How much will Daniel have after 2 years?
Answers
Answer:
I = $ 220.00
Step-by-step explanation:
I = $ 220.00
Equation:
I = Prt
Solve:
First, converting R percent to r a decimal
r = R/100 = 5%/100 = 0.05 per year,
then, solving our equation
I = 2200 × 0.05 × 2 = 220
I = $ 220.00
The simple interest accumulated
on a principal of $ 2,200.00
at a rate of 5% per year
for 2 years is $ 220.00.
19
Select the correct answer.
A developer buys an empty lot to build a small house. What is the area of the lot?
Answers
Area of the plot = 193 sq.yd. , Option B is the correct answer.
What is Area ?
Area is the space occupied by a flat surface or an object .
It is measured in square units
It has wide daily life importance like in the question mentioned , a plot will be measured in area of the space.
It is given that
A developer buys an empty lot to build a small house.
area of the lot = ?
The figure is incomplete and the complete figure is attached with the answer.
To determine the area the figure needs to be divided into triangles and rectangles as shown in the figure
Area of the first triangle = (1/2) * base * height
By Calculation
base = 17 unit and height = 10 unit
= (1/2) * 17 * 10
= 17*5
=85 sq.unit
Area of the second triangle = (1/2)* 9* 8
=36 sq. unit
Area of the rectangle = base * height
base = 9 unit and height = 7 unit
Area = 9*7= 63 sq.unit
Area of the last triangle = (1/2) * 2*9
= 9 unit
The area of the plot = 85+36+63+9
Area of the plot = 193 sq.yd.
Therefore , Option B is the correct answer.
To know more about Area
https://brainly.com/question/27683633
#SPJ1
Answer:
Step-by-step explanation:
Area of the plot = 193 sq.yd. , Option B is the correct answer.
What is Area ?
Area is the space occupied by a flat surface or an object .
It is measured in square units
It has wide daily life importance like in the question mentioned , a plot will be measured in area of the space.
It is given that
A developer buys an empty lot to build a small house.
area of the lot = ?
The figure is incomplete and the complete figure is attached with the answer.
To determine the area the figure needs to be divided into triangles and rectangles as shown in the figure
Area of the first triangle = (1/2) * base * height
By Calculation
base = 17 unit and height = 10 unit
= (1/2) * 17 * 10
= 17*5
=85 sq.unit
Area of the second triangle = (1/2)* 9* 8
=36 sq. unit
Area of the rectangle = base * height
base = 9 unit and height = 7 unit
Area = 9*7= 63 sq.unit
Area of the last triangle = (1/2) * 2*9
= 9 unit
The area of the plot = 85+36+63+9
Area of the plot = 193 sq.yd.
Therefore , Option B is the correct answer.
To know more about Area
brainly.com/question/27683633
#SPJ1
A cone has a diameter of 16 cm and a height of 35 cm. What is its volume?
Answers
Answer: if with 3.14 v= 37512.5333
if with pi v= 37531.56
Step-by-step explanation:
the formula is 1/3hπr^2
r= 2d so radius is 32
plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)
What is the surface area of the figure? 408ft^2 458ft^2 545ft^2 720ft^2
Answers
9514 1404 393
Answer:
(b) 458 ft²
Step-by-step explanation:
The total area is the sum of the L-shaped front and back areas and the areas of the 6 rectangular faces.
The front L-shaped area can be considered to be a 12 ft × 12 ft square with a 5 ft × 7 ft rectangle cut from the upper left corner. Its area is then ...
(12 ft)(12 ft) -(5 ft)(7 ft) = (144 -35) ft² = 109 ft² . . . . front area
__
The sum of the areas of the rectangular faces is the product of the width of the figure (5 ft) and the perimeter of the L-shaped face. That perimeter is the sum of the edge lengths. Starting from the lower-left corner and working clockwise, we find the perimeter to be ...
7 ft + 7 ft + 5 ft + 5 ft + 12 ft + 12 ft = 48 ft
Then the sum of rectangular face areas is ...
(48 ft)(5 ft) = 240 ft² . . . . rectangular face area
The total surface area is then ...
2×front area + rectangular face area
= 2×109 ft² +240 ft² = 458 ft² . . . . total surface area
Christian conducted a survey to find the favorite hobby of her classmates from 4 choices. He surveyed the same number of girls as boys. The table
shows his results
Name Number of Boys Number of Girls
Cooking
5
6
Drawing
4
5
Reading
10
10
Hiking
6
4
Which of the following statements about the data is true?
More girls than boys prefer hiking.
O Fewer students prefer reading than prefer cooking,
Twice as many sutdents prefer reading than prefer hiking,
The hobby that the most boys prefer is different than the hobby that most girls prefer
Answers
Answer:
Twice as many students prefer reading than prefer hiking,
Step-by-step explanation:
Combined reading is 20 and hiking is 10
Please give me the brainliest
Freddy went to the museum and bought a reduced copy of a painting he saw in a exhibit. If the actual painting is 12 inches high, how wide is it ?
Answers
Answer:
It is probably 6 inches wide. I tried my best
Step-by-step explanation:
Harris Interactive® conducted a poll of American adults in August of 2011 to study the use of online medical information. Of the 1,019 randomly chosen adults, 60% had used the Internet within the past month to obtain medical information. Use the results of this survey to create an approximate 95% confidence interval estimate for the percentage of all American adults who have used the Internet to obtain medical information in the past month.
Answers
Answer:
\(0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570\)
\(0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630\)
The 95% confidence interval for the true proportion would be given by (0.570;0.630) .
And if we convert this into % we got (57.0%, 63.0%)
Step-by-step explanation:
The information given we have the following info given:
\( n = 1019\) represent the sampel size
\( \hat p=0.6\) represent the sample proportion of interest
The confidence level is 95%, our significance level would be given by \(\alpha=1-0.95=0.05\) and \(\alpha/2 =0.025\). And the critical value would be given by:
\(z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96\)
The confidence interval for the mean is given by the following formula:
\(\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}\)
Replacing the info given we got:
\(0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570\)
\(0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630\)
The 95% confidence interval for the true proportion would be given by (0.570;0.630) .
And if we convert this into % we got (57.0%, 63.0%)
It cost $2,845.80 for 3 people to go on a sightseeing vacation to Washington DC. How much did it cost in dollars per person?
Answers
than 2,845.80
Answer:
It costs $948.60 per person
Step-by-step explanation:
When you divide 2,845.80 by 3 we get 948.6.
I hope this helps you in any way:)
20. Rafael has a business selling computers. He buys computers from the manufacturer for $450
each and sells them for $800. Each month, he must also pay fixed costs of $3000 for rent and
utilities at his store. If he sells n computers in a month, which of the following equations can be used
to calculate his profit?
A. P = n(800 - 450)
B. P = n(800 - 450 - 3000)
C. P = 3000n(800 - 450)
D. P = n(800 - 450) - 3000
E. P = n(800 - 450) + 3000
Yeah
Answers
Answer: D , p = n (800 - 450) - 3000
Step-by-step explanation: Firstly, you have to account for how much money Rafael is making off of each computer (800 - 450). That factor is then multiplied by the variable "n" which represents the amount of computers sold. Lastly, since this is an equation to calculate his monthly profits, you have to subtract the rent that he is paying ($3000) from the total profit that he made off of selling the computers. Therefore, giving you the equation
P (profit) = n (amount of computers sold) (800-450) - 3000 (rent).
The equation that represents Rafael's monthly profit selling 'n' numbers of computers is D. P = n(800 - 450) - 3000.
What is an equation?An equation represents equality for the terms that are on the both side of the equal sign.
Given Rafael buys computers for 450 dollars and sells them for 800 dollars each.
He also had to pay 3000 dollars for rent and utilities for the store and the number of computers sold in each month is given by 'n'.
∴ The equation that represents his profit(P) in a month is,
P = n(800 - 450) - 3000.
learn more about equations here :
https://brainly.com/question/10413253
#SPJ2
judy catches the 12:30 train from aberystwy
Answers
What is the range of the function y=3√√x+8 1x
Answers
Answer:
The range of the function is: -∞≤y≤∞.
Consider the provided function.
The range of the function is the set of all values which a function can produce or the set of y values which a function can produce after substitute the possible values of x.
The range of a cubic root function is all real numbers.
Now consider the provided function.
The above function can be written as:
Taking cube on both sides.
The graph of the function is shown in figure 1:
For any value of x we can find different value of y.
Here, the cube root function can process negative values. Since, the function can produce any values, the range of the given function is -∞≤y≤∞ .
Therefore, the range of the function is: -∞≤y≤∞ (A).
Does anyone know this? Needed ASAP
Answers
Answer:
50 square units
Step-by-step explanation:
Using the formula provided, \(a = \frac{1}{2}h(b_1+b_2)\), substituting the height (5), b1 (8) and b2 (12), we can solve for the formula.
\(a = \frac{1}{2}\cdot5(8+12)\\\\a = \frac{1}{2}\cdot5(20)\\\\a = \frac{1}{2}100\\\\a = 50\)
Hope this helped!
Answer:
50 units²
Step-by-step explanation:
The area of a trapezoid can be found using the following formula.
\(A=\frac{1}{2}h(b_{1} +b_{2} )\)
The height of the trapezoid is 5 units. The bases are 8 units and 12 units.
\(h= 5 \\b_{1} = 8\\b_{2} = 12\)
Substitute the values into the formula.
\(A=\frac{1}{2}*5(8+12)\)
Solve inside the parentheses. Add 8 and 12.
8+12=20
\(A=\frac{1}{2}*5(20)\)
Multiply 5 and 20.
5*20= 100
\(A=\frac{1}{2}*100\)
Multiply 1/2 and 100 or divide 100 by 2.
100 * 1/2= 50 or 100/2= 50
\(A= 50\)
Add appropriate units. For this problem, the units are units².
\(A= 50 units^2\)
The area of the trapezoid is 50 square units.
What's the distance between P(-4,3) and Q(6,1). Round to the nearest tenth
Answers
Answer:
\(d=10.2\)
Step-by-step explanation:
Distance Formula: \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Simply plug in the 2 coordinates into the distance formula to find distance d:
\(d=\sqrt{(6-(-4))^2+(1-3)^2}\)
\(d=\sqrt{(6+4)^2+(-2)^2}\)
\(d=\sqrt{(10)^2+4}\)
\(d=\sqrt{100+4}\)
\(d=\sqrt{104}\)
\(d=2\sqrt{26}\)
\(d=10.198\)
\(d=10.2\)
Ivan and Tanya share £150 in the ratio 4:1 Work out how much more Ivan gets compared to Tanya.
Answers
Answer:
Ivan get 90 pounds more than Tanya.
Step-by-step explanation:
Since it's a 4:1 ratio there is 5 parts in total. So i divided the 150 by 5 to get 30. From there i multiplies the 30 by 4 to get Ivan's portion and Tanya only has one portion which is 30. So Ivan has 120 and Tanya has 30, 120-30= 90
Answer:
Ivan gets 120 and Tanya gets 30
Step-by-step explanation:
4 plus 1 is 5. 150 divided by 5 is 30 (Tanya's share) and 150 minus 30 is 120(Ivan's share)
Which of the following is an equivalent
simplified expression for
3(2x + 1) - 2(4x - 1)
A. 2x + 1
B. -2x + 5
C. -X + 5
D. 14x + 1
E. 14x - 1
Answers
Answer:
B. -2x + 5
Step-by-step explanation:
First, distribute the 3 and 2 to the parentheses:
3(2x + 1) - 2(4x - 1)
6x + 3 - 8x + 2
Add like terms:
-2x + 5
So, the simplified expression is -2x + 5
B is the correct answer
Answer:
it is B
Step-by-step explanation:
3*2x=6x
2*4x=8x
1*3=3
1*2=2
6x-8x= -2x
3+2=5
i got the +2 because there are two negative signs and that makes it positive
If h(x) = 6 – x, what is the value of (h circle h) (10)?
Answers
Answer:
10
Step-by-step explanation:
hoh(x) = h(h(x)) = 6 - h(x) = 6 - (6-x) = 6 - 6 + x = x
then
hoh(x) = x
then
hoh(10) = 10
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 130 engines and the mean pressure was 4.2 lbs/square inch. Assume the variance is known to be 0.49. If the valve was designed to produce a mean pressure of 4.3 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs below the specifications?
State the null and alternative hypotheses for the above scenario.
Answers
An engineer has designed a valve that will regulate water pressure on an automobile engine. There is not enough evidence to conclude the claim.
H:µ= 4.3
Ha:µ < 4.3 (left-tailed)
n = 43
\(\bar{x} = 4.2\)
σ = 0.7
α = 0.02
Standard error, S.E \(= \frac{\sigma}{\sqrt{n}}\)
\(= \frac{0.7}{\sqrt{4.3}}\)
= 0.1067
Test statistic: \(Z = \frac{(\bar{x} - \mu)}{S.E}\)
= (4.2 - 4.3) / 0.1067
= -0.94
p-value = 0.1736 (from z-table) or
[excel command:
=NORM.S.DIST(z,1)]
since, p-value > α , do not reject H
There is not enough evidence to conclude the claim.
Learn more about pressure here; https://brainly.com/question/13373498
#SPJ1
13
A number cube with faces numbered 1-6 is rolled,
Determine whether each statement correctly describes the likelihood of an event based on the given number cube.
Select True or False for each statement.
It is likely that a number greater than 2 is obtained on the number cube.
It is unlikely that a number less than 4 is obtained on the number cube.
It is certain that an odd or even number is obtained on the number cube.
It is unlikely that a number less than 5 is obtained on the number cube.
True False
Answers
Answer: True - There are four numbers greater than 2 (3, 4, 5, and 6) out of a total of six possible outcomes, making it likely that a number greater than 2 will be obtained.
False - There are three numbers less than 4 (1, 2, and 3) out of a total of six possible outcomes, making it likely that a number less than 4 will be obtained.
True - All numbers on the cube are either odd or even, so it is certain that an odd or even number will be obtained.
True - There are only two numbers less than 5 (1 and 2) out of a total of six possible outcomes, making it unlikely that a number less than 5 will be obtained.
Find the side length of a cube with a volume of 141 f3 If necessary, round your answer to the nearest tenth.
Answers
The side length of the cube is 5.6 feet (rounded to the nearest tenth).
We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.
We can calculate s by taking the cube root of both sides of the equation:
\(s = (V)^{(1/3)\)
Substituting V = 141, we get:
\(s = (141)^{(1/3)\)
By using a calculator to evaluate this expression, we may determine:
s ≈ 5.6
As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.
for such more question on length
https://brainly.com/question/20339811
#SPJ11
Which expression is equivalent to 6^-6 x 6^6
Answers
Answer:
Step-by-step explanation:
x^-3 * x^-3
what two numbers have a GCF of 5 and a LCM of 50
Answers
Answer:
10 and 5
Step-by-step explanation:
The video exchange video store recorded a loss of $1,530.00 over a period of 6 months. What was the average change per month .
Answers
Answer: 255
Step-by-step explanation:1530/6= 255
Solve the following equation by first writing the equation in the form ax² = c
²-49-0
a.
b.
C.
d.
-49
- 149
= 7
:= ±7
Answers
The solution to the given equation is x = ±7. The correct option is d. x = ±7
Solving quadratic equationsFrom the question, we are to determine the solution to the given equation
The given equation is
x²-49 = 0
NOTE: I assumed the variable is x
Solving the equation
x²-49 = 0
Writing in the form ax²= c
x² = 49
∴ x = ±√49
x = ±7
Hence, the solution to the given equation is x = ±7
Learn more on Solving quadratic equations here: https://brainly.com/question/24334139
#SPJ1
Find the value of y.
Answers
The value of y is 4√3
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.
Also , the ratio of corresponding sides of similar triangles are equal.
There are two triangles that are similar
Therefore;
y /16 = 4/y
y² = 48
y = √48
y = √16 × √ 3
y = 4√3
Therefore, the value of y is 4√3
learn more about similar triangles from
https://brainly.com/question/14285697
#SPJ1
At the district competition for 5th grade jump-roper of the year, the following number of jumps were recorded per student:
203, 245, 237, 233, 90, 100, 100, 277, 265, 264, 265, 285, 288, 291, 291, 290, 300, 224, 200, 257, 290, 279, 266, 288
What is the mean number of jumps, rounded to the nearest hundredth?
What is the median number of jumps?
Answers
At the district competition for 5th grade jump-roper of the year, the mean number of jumps, rounded to the nearest hundredth is 242.83 and the median number of jumps is 265
The mean can be calculated as follows:
Observations (the number of jumps each student without pausing was counted); There were 24 observations
Mean is calculated by adding all of the observations together.
Mean = (203 + 245 + 237 + 233 + 90 + 100 + 100 + 277 + 265 + 264 + 265 + 285 + 288 + 291 + 291 + 290 + 300 + 224 + 200 + 257 + 290 + 279 + 266 + 288)/24
Mean = 5828/24
Mean = 242.83
to figure out the median;
The observations must first be put into either ascending or descending order.
Ordered in descending order
90, 100, 100, 200, 203, 224, 233, 237, 245, 257, 265, 265, 265, 266, 277, 279, 285, 288, 288, 290, 290, 291, 291, 300
Given that there have been 24 observations (an even number).
The middle number, 265 and 265 at the midway of items 12 and 13, is used to calculate the median.
The average of these figures is then determined.
Median = 1/2 (265 + 265)
Median = 265
Learn more about mean at https://brainly.com/question/16582452
#SPJ4
Write the point-slope form of an equation of the line through the points (-2, 6) and (3, -2).A. y+2=−85(x+3)
B. y−3=−85(x+2)
C. y−6=−85(x+2)
D. y+2=−85(x−6)
Answers
The equation in point slope form is y - 6 = -8/5(x + 2)
How to determine the linear equation?The points are given as:
(-2, 6) and (3, -2)
Start by calculating the slope (m) using:
m = (y2 - y1)/(x2 - x1)
This gives
m = (-2 - 6)/(3 + 2)
Evaluate
m = -8/5
The linear equation is then calculated using:
y - y1 = m(x - x1)
This gives
y - 6 = -8/5(x + 2)
Hence, the equation in point slope form is y - 6 = -8/5(x + 2)
Read more about linear equations at:
https://brainly.com/question/14323743
#SPJ1
in a data set consisting of 30 positive integers, the minimum value is 13. the number 6 is added to the original set to create a set of 31 positive integers. which of the following measures must be 7 greater for the new data set than for the original data set?
a. The mean
b. The median
c. The range
d. The standard deviation
Answers
The mean, median, range, and standard deviation for the new data set must all be 7 greater than for the original data set.
The mean is the sum of all the values divided by the number of values. Adding the number 6 to the original data set of 30 positive integers increases the sum of all the values by 6, which means the mean for the new data set must be 7 greater than the mean for the original data set.
The formula for the mean is: Mean = (Sum of Values)/(Number of Values)
For the original data set: Mean = (Sum of Values)/30
For the new data set: Mean = (Sum of Values + 6)/31
Therefore, the mean for the new data set must be 7 greater than the mean for the original data set.
The median is the middle value in a set of data. Adding the number 6 to the original data set of 30 positive integers increases the total number of values to 31, which means the median is calculated differently for the new data set than the original data set. The median for the new data set must be 7 greater than the median for the original data set.
The formula for the median is: Median = (n+1)/2
For the original data set: Median = (30+1)/2 = 15.5
For the new data set: Median = (31+1)/2 = 16.5
Therefore, the median for the new data set must be 7 greater than the median for the original data set.
The range is calculated by subtracting the smallest value from the largest value in a data set. Adding the number 6 to the original data set of 30 positive integers increases the largest value by 6, which means the range for the new data set must be 7 greater than the range for the original data set.
The formula for the range is: Range = (Largest Value) - (Smallest Value)
For the original data set: Range = (Largest Value) - 13
For the new data set: Range = (Largest Value + 6) - 13
Therefore, the range for the new data set must be 7 greater than the range for the original data set.
The standard deviation is a measure of how spread out the values in a data set are. Adding the number 6 to the original data set of 30 positive integers increases the total number of values by 1, which means the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.
The formula for the standard deviation is: Standard Deviation = √ (Sum of (Values - Mean)2 / Number of Values)
For the original data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 30)
For the new data set: Standard Deviation = √ (Sum of (Values - Mean)2 / 31)
Therefore, the standard deviation for the new data set must be 7 greater than the standard deviation for the original data set.
The mean, median, range, and standard deviation for the new data set must all be 7 greater than for the original data set
Learn more about standard deviation here:
https://brainly.com/question/23907081
#SPJ4