Answer:
The number of false positives is 108. The right answer is A
Step-by-step explanation:
According to the given data we have the following:
probability of negative results which are correcly identified =0.7
probability of negative results which are wrongly identified =1-0.7 =0.3
hence, probability of negative result = 1-0.1 =0.9
Therefore, in order to calculate the number of false positives we would have to use the following formula:
false positives =total number * probability of negative results which are wrongly identified * probability of negative result=400 * 0.9*(1-0.7) = 108
false positives = 400 * 0.9*(1-0.7)
false positives = 108
The number of false positives is 108
BoxedNGone truck rentals calculates that its price function is p(x) = 200 − 2x, where p is the price (in dollars) at which exactly x trucks will be rented per day. Find the number of trucks that BoxedNGone should rent and the price it should charge to maximize revenue. Also find the maximum revenue.
Answer:
At Maximum point;
x(max) = 50
p(max) = $100
Maximum revenue = $5,000
Step-by-step explanation:
The price function is;
p(x) = 200 − 2x
where
p is the price (in dollars) at which exactly x trucks will be rented per day.
The revenue function R(x) can be written as;
R(x) = p(x) × x
Substituting p(x) equation;
R(x) = (200-2x)x
R(x) = 200x-2x^2 ........1
To maximize R(x), at maximum point dR/dx = 0
differentiating equation 1;
dR/dx = 200 - 4x = 0
4x = 200
x = 200/4
x = 50
Substituting x = 50 into p(x)
p(50) = 200 - 2(50) = $100
p = $100
Maximum revenue is;
R = p × x = $100×50
R = $5,000
At the level of the maximum point, the value of x(max) should be 50 and the value of p(max) should be $100, Also, Maximum revenue = $5,000.
Calculation of the maximum value:Since
The price function is;
p(x) = 200 − 2x
Here,
p refer to the price (in dollars) at which exactly x trucks should be rented per day.
Now
The revenue function R(x) should be
R(x) = p(x) × x
Now
R(x) = (200-2x)x
R(x) = 200x-2x^2 ........1
Now
To maximize R(x), at maximum point dR/dx = 0
So,
dR/dx = 200 - 4x = 0
4x = 200
x = 200/4
x = 50
Now
Substituting x = 50 into p(x)p(50) = 200 - 2(50) = $100
p = $100
Now
Maximum revenue is;
R = p × x = $100×50
R = $5,000
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At a point on the ground 46 feet from the foot of a tree, the angle of elevation to the top of the tree is 68°. What is the height of the tree?
Final answer:
The height of the tree is approximately 113.85 feet, which is determined by using the tangent of the given angle of elevation (68°) and the distance from the tree (46 feet) in a trigonometric calculation.
Explanation:
To find the height of the tree, we can use trigonometry. The student is 46 feet from the tree, and the angle of elevation to the top of the tree is 68°. The height of the tree can be found using the tangent function in a right triangle, where the opposite side is the tree height (h), and the adjacent side is the distance from the tree (46 feet). The tangent of the angle of elevation (θ) is the ratio of the opposite side to the adjacent side.
So, tan(68°) = h / 46 feet. To find the height (h), multiply both sides by 46 feet:
h = 46 feet × tan(68°)
We can use a calculator to find that tan(68°) is approximately 2.475. Now, multiply 46 feet by this tangent value to get the height:
h = 46 feet × 2.475h = 113.85 feet (rounded to two decimal places)
Therefore, the height of the tree is approximately 113.85 feet.
What is the expression for the quotient of z and 4
Answer:
[tex]\dfrac{z}{4}\text{ or }z/4\text{ or }z\div 4[/tex]
Step-by-step explanation:
"The quotient of z and 4" means "z divided by 4." That can be written several ways, as shown above.
What is the slope of (0,4) and (-4,-3)
Step-by-step explanation:
Given points
( x1 , y1 ) = ( 0, 4)
And
( x2 , y2 ) = ( - 4 , - 3 )
Now
Slope(m)
= ( y2 - y1 ) / ( x2 - x1 )
= ( - 3 - 4) / ( -4 - 0)
= - 7 / - 4
= 7/4
Answer:
m=7/4
Step-by-step explanation:
Solving exponential equations with a common base problem in the picture!
Given:
The given expression is [tex]18^{x^{2}+4 x+4}=18^{9 x+18}[/tex]
We need to determine the solution of the given expression.
Solution:
Let us solve the exponential equations with common base.
Applying the rule, if [tex]a^{f(x)}=a^{g(x)}[/tex] then [tex]f(x)=g(x)[/tex]
Thus, we have;
[tex]x^{2}+4 x+4=9 x+18[/tex]
Subtracting both sides of the equation by 9x, we get;
[tex]x^{2}-5 x+4=18[/tex]
Subtracting both sides of the equation by 18, we have;
[tex]x^{2}-5 x-14=0[/tex]
Factoring the equation, we get;
[tex]x^2-7x+2x-14=0[/tex]
Grouping the terms, we have;
[tex](x^2-7x)+(2x-14)=0[/tex]
Taking out the common term from both the groups, we get;
[tex]x(x-7)+2(x-7)=0[/tex]
Factoring out the common term (x - 7), we get;
[tex](x+2)(x-7)=0[/tex]
[tex]x+2=0 \ and \ x-7=0[/tex]
[tex]x=-2 \ and \ x=7[/tex]
Thus, the solution of the exponential equations is x = -2 and x = 7.
Hence, Option C is the correct answer.
A bacteria doubles its original population in 16 hours (A=2A0). How big will its population be in 96 hours?
Answer:
The population will be 64 times larger after 96 hours.
Leave a comment if you'd like a more in-depth explanation.
Answer:
64 times as large as the original population.
Step-by-step explanation:
A road crew takes 1/5 of an hour to pave five miles of road how long will it takes the crew to pave one mile of road
Each day, a factory produces a total of 280 containers of ice cream. The flavors are vanilla, chocolate, and strawberry. Each day, the factory produces twice as much chocolate ice cream as strawberry ice cream and 20 more containers of vanilla ice cream than strawberry ice cream.What is the correct equation, and what is the correct solution, for this situation, where s represents the number of containers of strawberry ice cream produced per day
Answer:
The correct equation in terms of s is: 4s=260
The number of strawberry ice cream produced per day, s=65.The number of chocolate ice cream produced per day ,c=130. The number of vanilla ice cream produced per day ,v=85.Step-by-step explanation:
Let the number of containers of strawberry ice cream produced per day=s
Let the number of containers of vanilla ice cream produced per day=v
Let the number of containers of chocolate ice cream produced per day=c
Total Number of Ice Cream Containers=280
s+v+c=280Given:
The factory produces twice as much chocolate ice cream as strawberry ice cream. This is written as:
c=2sThe factory produces 20 more containers of vanilla ice cream than strawberry ice cream. This is written as:
v=s+20Therefore substituting c=2s and v=s+20 into the first equation: s+v+c=280
s+s+20+2s=280
4s=280-20
4s=260
Divide both sides by 4
s=65
The number of strawberry ice cream produced per day is 65.
The number of chocolate ice cream produced per day =2s=2(65)=130.
The number of vanilla ice cream produced per day =s+20=65+20=85.
Final answer:
The number of containers of strawberry ice cream produced per day is 65.
Explanation:
The question is asking us to find the correct equation and solution for the number of containers of strawberry ice cream produced per day by a factory, while taking into account that chocolate is produced at twice the rate and vanilla at 20 more containers than strawberry.
Given the total production is 280 containers, the equation can be set up as follows:
s + 2s + (s + 20) = 280,
where s represents the number of strawberry ice cream containers produced per day.
Step-by-step, we can solve this equation:
Add up the s terms: s + 2s + s = 4s.Substitute the sum into the original equation: 4s + 20 = 280.Subtract 20 from both sides: 4s = 260.Divide both sides by 4: s = 65.Therefore, the factory produces 65 containers of strawberry ice cream per day.
What are the roots of y=x2-3x-10
Answer:
x = 5 and -2
Step-by-step explanation:
This question wants the roots, which are when y = 0.
Set the equation equal to 0:
y=x2-3x-10
0=x2-3x-10
Now we can factor this (or use our calculators).
0=(x-5)(x+2)
Separate these by the Zero Product Property.
0 = x-5
x = 5
0 = x+2
x = -2
Answer:
-2 and 5
b on edu 2020
Step-by-step explanation:
edu 2020
Delicious Candy markets a two-pound box of assorted chocolates. Because of imperfections in the candy making equipment, the actual weight of the chocolate has a uniform distribution ranging from 31.8 to 32.6 ounces. a. Define a probability density function for the weight of the box of chocolate. b. What is the probability that a box weighs (1) exactly 32 ounces; (2) more than 32.3 ounces; (3) less than 31.8 ounces? c. The government requires that at least 60% of all products sold weigh at least as much as stated weight. Does Delicious Candy violate government regulation?
Answer:
a. [tex]f(x)= 1.25\ \ \ \ , \ for \ 31.8\leq x\leq 32.6[/tex]
[tex]b. \ P(X=32)=0\\P(X>32.3)=0.375\\P(X<31.8)=0[/tex]
c. No. Delicious Candy isn't violating any government regulations
Step-by-step explanation:
a.
-A uniform distribution is given by the formula:
[tex]f(x)=\frac{1}{b-a} \ \ \ for \ \ \ a\leq x\leq b[/tex]
#we substitute our values in the formula above to determine the distribution:
[tex]f(x)=\frac{1}{b-a}\\\\=\frac{1}{32.6-31.8}\\\\=1.25\\\\\therefore f(x)=1.25, \ \ \ 31.8\leq x\leq 32.6[/tex]
Hence, the probability density function for the box's weight is given as: [tex]f(x)=1.25, \ \ \ 31.8\leq x\leq 32.6[/tex]
b. The probability of the box's weight being exactly 32 ounces is obtained by integrating f(x) over a=b=32:
[tex]f(x)=1.25, \ \ \ a\leq x\leq b\\\\=\int\limits^{32}_{32} {1.25} \, dx \\\\\\=[1.25x]\limits^{32}_{32}\\\\\\=1.25[32.0-32.0]\\\\\\=0[/tex]
Hence, the probability that a box weighs exactly 32 ounces is 0.000
ii.The probability that a box weighs more than 32.3 is obtained by integrating f(x) over the limits 32.3 to 32.6 :
[tex]f(x)=1.25, \ \ \ a\leq x\leq b\\\\=\int\limits^{32.6}_{32.3} {1.25} \, dx \\\\\\=[1.25x]\limits^{32.6}_{32.3}\\\\\\=1.25[32.6-32.3]\\\\\\=0.375[/tex]
Hence, the probability that a box weighs more than 32.3 ounces is 0.3750
iii. The probability that a box weighs less than 31.8 is 0.000 since the weight limits are [tex]31.8\leq x\leq 32.6[/tex].
-Any value above or below these limits have a probability of 0.000
c. Let 32 ounces be the government's stated weight.
[tex]1.25(32.6-32)=0.75\\\\0.75>0.60[/tex]
Hence, Delicious Candy isn't violating any government's regulations.
(a): The required probability density function for the weight of the box of chocolate is 1.25
(b): The probability that a box weighs (1) exactly 32 ounces is 0
and (2) more than 32.3 ounces is 0.375
(c): Therefore, Delicious Candy does not violate government regulation.
Probability:Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. Probability can range in from 0 to 1.
Given that,
The uniform distribution between [tex]a = 31.8[/tex] ounce and [tex]b = 32.6[/tex] ounce
Part(a):
The probability density function for the weight of the box of chocolate is,
[tex]\frac{1}{b-a}=\frac{1}{32.6-31.8} \\=1.25[/tex]
Part(b):
(1) P(exactly 32 ounces) = 0, because this is a continuous distribution.
(2) P(more than 32.3 ounces) =[tex]1.25\times (32.6-32.3)=0.375[/tex]
Part(c):
The stated weight of Delicious Candy = 2 pounds
That is, [tex]2\times 16=32[/tex] ounces
P(a candy weigh at least as much as stated) = P(at least 32)
[tex]1.25\times (32.6-32)=0.75[/tex]
So, 75% of candies weigh at least as much as stated.
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Mr. Jackson filled up his 15-gallon gas tank for $37.50. What was the price 10
of gas per gallon?
Answer:
[tex]Unit Price =\$2.5 \:per\: gallon[/tex]
Step-by-step explanation:
15 Gallon of Gas costs $37.50
To determine the Unit Price, we divide the Total Cost by the number of gallons of gas bought.
Unit Price
[tex]=\dfrac{\$37.50}{15gallons}\\Unit Price =\$2.5 \:per\: gallon[/tex]
Answer:
Price per gallon = $2.5 per gallon
Step-by-step explanation:
Given;
Price of 15 gallons = $37.50
Number of gallons = 15
Price per gallon = 37.50/15 = $2.5
2. a) Find the break - even points for company X, which sells all it produces, if the
variable cost per unit is $3, fixed costs are $2 and Yrr = 5/9, where q is the number
of thousands of units of output produced.
b) Graph the total revenue curve and the total cost curve in the same plane.
c) Use your answer in (a) to report the quantity interval in which maximum profit
occurs.
Show all steps to get full credit. Solve it Algebraically
Find the solution in the attachments
In this exercise we have to use the knowledge of finance and thus plot a graph, this way we have that it corresponds to:
A)[tex]q= 0 \ or \ q=1[/tex]
B) The graph bellow.
C) The points of the grapg bellow.
Knowing that:
[tex]total \ cost = (variable \ cost \ per \ unit + final \ cost \ per \ unit * produced)[/tex]
The data that was informed is;
Variable cost por unit: 3Linear cost per unit: 2Units produced : 9A) The result is:
[tex]T= (3+2)*9\\T= 59[/tex]
Break even points one the points at which total cost are equal to :
[tex]T(q)= Y_T(9)\\5q= 5\sqrt{9}\\q=\sqrt{9}\\ q= 0 or q=1[/tex]
B) One plot of total cost are total revenue are ploted below. The blue curve is of total revenue and real graph is of total cost.
C) With the graph, it's closes that from q=0 ot q=1. Total revenue dominantes total cost and beyond a=1 the total cost dominands total revenue.
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What is the correct name for the angle shown
Answer:
i dont see no angle
Step-by-step explanation:
Angles can be named according to their measure in degrees or position on a plane. Angles are always counted to be positive in the counter-clockwise direction and negative in the clockwise direction.
Explanation:The name of an angle in Mathematics can vary based on its measure and location. Angles are generally named according to their measure in degrees, and they can be categorized as acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (180 degrees), reflex (greater than 180 degrees), or full (360 degrees).
Angles can also be referred to in terms of their position on a Cartesian plane: angles in the first quadrant are positive and less than 90; in the second quadrant, they are more than 90 but less than 180; in the third quadrant, they exceed 180 but are less than 270; and in the fourth quadrant, they are greater than 270 but less than 360 degrees.
This consistently maintains the rule that angles are defined as positive in the counter-clockwise direction, and negative in the clockwise direction. For example, an angle of 30° south of west is the same as the global angle 210°, or it can also be expressed as −150° relative to the positive x-axis.
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Six men and four women are waiting to be interviewed for jobs. If they are all selected in random order, find the probability that no man will be interviewed until at least two women have been interviewed.
Answer:
The correct answer is 0.1714 .
Step-by-step explanation:
There are 6 men and 4 women to be interviewed for jobs.
Total number of arrangements in which they can be called for the interview process is 10!.
Number of ways any two women are interviewed before any man is 4 × 3 × 8!. = 12 × 8!.
Number of ways any three women are interviewed before any man is 4 × 3 × 2 × 7!. = 24 × 7!.
Number of ways all the women are interviewed before any man is 4! × 6!.
Required number of ways in which at least two women being interviewed before any man is given by 12 × 8! + 24 × 7! + 4! × 6! = 864 × 6!.
Required probability is 864 × 6! ÷ 10! = 0.1714
The probability that no man will be interviewed until at least two women have been interviewed is [tex]\( \bxed{\frac{2}{15}} \).[/tex]
Step 1
We may utilise the concept of permutations to estimate the likelihood that no man will be interviewed until at least two women have been interviewed.
Let us examine the case where a minimum of two women are interviewed before a guy is examined. This implies that women must have the first two places in the interview process. Men and women may be appointed to the other positions in any order, following these two positions.
Let's figure out how many options there are to choose the first two slots for women, given that there are four women and six men:
Step 2
Number of ways to select the first woman: [tex]\(4\)[/tex]
Number of ways to select the second woman: [tex]\(3\)[/tex] (since one woman has already been selected for the first position)
The total number of ways to select the first two positions for women is [tex]\(4 \times 3 = 12\).[/tex]
Step 3
After these two positions have been filled with women, the remaining 8 positions (6 men + 2 women) can be filled with the remaining people (4 men + 2 women) in any order. This can be calculated using the permutation formula:
[tex]\[ nPr = \frac{{n!}}{{(n-r)!}} \][/tex]
Where n is the total number of people and r is the number of positions to be filled.
For our scenario, [tex]\( n = 6 + 4 = 10 \)[/tex] and [tex]\( r = 8 \)[/tex]. So, the number of ways to fill the remaining 8 positions is:
[tex]\[ 10P8 = \frac{{10!}}{{(10-8)!}} = \frac{{10!}}{{2!}} = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \][/tex]
Step 4
Now, let's calculate the total number of ways to select the positions for all 10 people:
[tex]\[ 10! \][/tex]
Consequently, the ratio of the number of favourable results to the total number of outcomes represents the likelihood that no guy will be interviewed until at least two women have been interviewed:
[tex]\[ \text{Probability} = \frac{{12 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3}}{{10!}} \]\[ \text{Probability} = \frac{{12}}{{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}} \]\[ \text{Probability} = \frac{{12}}{{10!/(10-8)!}} \]\[ \text{Probability} = \frac{{12}}{{10P8}} \]\[ \text{Probability} = \frac{{12}}{{10 \times 9}} \]\[ \text{Probability} = \frac{2}{15} \][/tex]
So, the probability that no man will be interviewed until at least two women have been interviewed is [tex]\( \bxed{\frac{2}{15}} \).[/tex]
The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.8 years and a standard deviation of 0.4 years. He then randomly selects records on 44 laptops sold in the past and finds that the mean replacement time is 3.6 years.
Assuming that the laptop replacement times have a mean of 3.8 years and a standard deviation of 0.4 years, find the probability that 44 randomly selected laptops will have a mean replacement time of 3.6 years or less.
P(¯¯¯X≤3.6 years)P(X¯≤3.6 years) = Round to 4 decimal places.
NOTE: Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted. Based on the result above, does it appear that the computer store has been given laptops of lower than average quality?
No. The probability of obtaining this data is greater than 5%, high enough to have been a chance occurrence.
Yes. The probability of obtaining this data is less than 5%, so it is unlikely to have occurred by chance alone.
Answer:
Probability that the 44 randomly selected laptops will have a mean replacement time of 3.6 years or less is 0.0092.
Yes. The probability of obtaining this data is less than 5%, so it is unlikely to have occurred by chance alone.
Step-by-step explanation:
We are given that the replacement times for the model laptop of concern are normally distributed with a mean of 3.8 years and a standard deviation of 0.4 years.
He then randomly selects records on 44 laptops sold in the past and finds that the mean replacement time is 3.6 years.
Let [tex]\bar X[/tex] = sample mean replacement time
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean replacement time = 3.8 years
[tex]\sigma[/tex] = standard deviation = 0.4 years
n = sample of laptops = 44
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, Probability that the 44 randomly selected laptops will have a mean replacement time of 3.6 years or less is given by = P([tex]\bar X[/tex] [tex]\leq[/tex] 3.6 years)
P([tex]\bar X[/tex] [tex]\leq[/tex] 3.6 years) = P( [tex]\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }[/tex] [tex]\leq[/tex] [tex]\frac{3.6-3.8}{\frac{0.4}{\sqrt{44} } }} }[/tex] ) = P(Z [tex]\leq[/tex] -3.32) = 1 - P(Z < 3.32)
= 1 - 0.99955 = 0.0005 or 0.05%
So, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 3.32 in the z table which has an area of 0.99955.
Hence, the required probability is 0.0005 or 0.05%.
Now, based on the result above; Yes, the computer store has been given laptops of lower than average quality because the probability of obtaining this data is less than 5%, so it is unlikely to have occurred by chance alone.
There are 805 lockers in the athletic center and 4026 students who need lockers. Therefore, some students must share lockers. What is the largest number of students who must necessarily share a locker
Answer:
6
Step-by-step explanation:
Data provided as per the question below:-
Number of students = 4025
Lockers = 805
The calculation of the largest number of students who must necessarily share a locker is shown below:-
Largest number of students = ((Number of students - 1) ÷ Lockers) + 1
= ((4026 - 1) ÷ 805) + 1
= (4025 ÷ 805) + 1
= 5 + 1
= 6
Can someone help me please
Answer:
1 unit
Step-by-step explanation:
If the circumference is 6, then the arc measured by a 60 degree angle, which is 1/6 of 360, represents 1/6 of the total circumference. Thus the answer is 1.
Estimate the solution to the system of equations, y = 4x-2 and y = x+3.
Answer:
x = 1.67 about and y = 4.67 about
Step-by-step explanation:
y = 4x-2 and y = x+3
4x - 2 = x + 3
3x = 5
x = 5/3 = 1.67 about
y = 5/3 + 3 = 5/3 + 9/3 = 14/3 = 4.667
A survey of 1060 randomly selected US teens ages 13 to 17 found that 605 of them say they have made a new friend online
The question discusses a survey of US teens and their online interaction. It's emphasizing on the statistical data that shows approximately 57% of surveyed teens reported making new friends online. Other data are also relevant to highlight various aspects of teens internet usage.
Explanation:The question is about a survey conducted on US teens, where 1060 were randomly selected and it was found that 605 of them have made a new friend online. This is relevant to statistics, a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.
To calculate the percentage of teens making friends online, it is calculated as follows: (Number of teens reporting making new friends online / Total number of teens surveyed) * 100 = (605/1060) * 100 = 57.08%. This implies that approximately 57% of the surveyed teens reported making new friends online.
The other data provided discuss various aspects of teen internet usage, including use of social media, smartphone adoption, and experiences with digital relationships. The given data can be used to set up and test various statistical hypotheses about teen behavior relating to internet use.
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Emma tiled a rectangle and then sketched her work. Write a multiplication equation to find the area of Emma's rectangle?
I was wondering if I was correct (my work) -
A = l x w
A = 3 1/2 units x 2 units
A = 7 units
Answer:
[tex]A=7 \: Square\: Units[/tex]
Step-by-step explanation:
From your work here, if the diagram corresponds with what was tiled, then:
Length of the Rectangle=[tex]3\frac{1}{2} \:Units[/tex]
Width of the Rectangle =2 Units
We know that:
Area of a Rectangle = Length X Width
[tex]=3\frac{1}{2} X 2\\A=7 \: Square\: Units[/tex]
The only thing wrong is the unit of the area given. The unit of area is supposed to be in Square Units.
Simplify the expression 4×3+4×x
Answer:
12+4x
Step-by-step explanation:
Evaluate 2x for x = 7
Answer:
Step-by-step explanation:
x = 7
so 2x is 2 x 7
The answer is 14
Answer:
14
Step-by-step explanation:
when x is 7 then 2x is 7*2
7*2=14
Ms. Smith took her bird to the vet. Tweety weighed 1 and 3/10 pounds. The vet said that tweety weighed 4/10 pounds more last year. How much did tweety weigh last year?
Answer:
1 and 7/10 pounds
Step-by-step explanation:
add.
Answer:
1 and 7/10 pounds
Step-by-step explanation:
A square matrix A is idempotent if A2=A. Let V be the vector space of all 2×2 matrices with real entries. Let H be the set of all 2×2 idempotent matrices with real entries. Is H a subspace of the vector space V?
Answer:
No, H is not a subspace of the vector space V.
Step-by-step explanation:
A matrix is a rectangular array in which elements are arranged in rows and columns.
A matrix in which number of columns is equal to number of rows is known as a square matrix.
Let H denote set of all 2×2 idempotent matrices.
H is a subspace of a vector space V if [tex]u+v \in H[/tex] for [tex]u,v \in V[/tex] and [tex]cu \in H[/tex].
Let [tex]A=\begin {pmatrix}1&0\\0&1 \end{pmatrix}[/tex]
As [tex]A^2=A\times A=\begin {pmatrix}1&0\\0&1 \end{pmatrix}\begin {pmatrix}1&0\\0&1 \end{pmatrix}=\begin {pmatrix}1&0\\0&1 \end{pmatrix}=A[/tex], A is idempotent.
So, [tex]A \in H[/tex]
[tex]A+A=\begin {pmatrix}1&0\\0&1 \end{pmatrix}+\begin {pmatrix}1&0\\0&1 \end{pmatrix}=\begin {pmatrix}2&0\\0&2\end{pmatrix} \\ \left ( A+A \right )^2=\begin {pmatrix}2&0\\0&2\end{pmatrix}\begin {pmatrix}2&0\\0&2\end{pmatrix}=\begin {pmatrix}4&0\\0&4\end{pmatrix}\neq A[/tex]So, A+A is not idempotent and hence, does not belong to H.
So, H is not a subspace of the vector space V.
Yes, H is a subspace of the vector space V. It satisfies the conditions of closure under addition, closure under scalar multiplication, and contains the zero vector.
Explanation:Yes, H is a subspace of the vector space V. In order for a set to be considered a subspace, it must satisfy three conditions: it must be closed under addition, closed under scalar multiplication, and contain the zero vector. Let's check if H satisfies these conditions:
Closed under addition: If A and B are idempotent matrices, then (A + B)^2 = (A + B)(A + B) = A^2 + AB + BA + B^2 = A + B, which means that (A + B) is also idempotent. So, H is closed under addition. Closed under scalar multiplication: If A is an idempotent matrix and k is a scalar, then (kA)^2 = (kA)(kA) = k^2(AA) = k^2A = kA, which means that kA is also idempotent. So, H is closed under scalar multiplication. Contains the zero vector: The zero matrix, which is the matrix with all entries equal to 0, is idempotent since 0^2 = 0. So, H contains the zero matrix, and therefore the zero vector.
Since H satisfies all three conditions, it is a subspace of the vector space V.
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convert 11 pi /6 radians to degrees
Answer:
330 degrees.
Step-by-step explanation:
π radians / 180 degrees = 1
(11 π)/6 radians * 180 / π = 11 * 180 / 6 = 11 * 30 = 330 degrees.
After converting into degree we get;
⇒ 11 pi /6 radians = 330 degree
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
The expression is,
⇒ 11 pi /6 radians
Now, To change into degree we can multiply by 180 / π in the given expression as;
⇒ 11 pi /6 radians
⇒ 11 π /6 × 180 / π degree
⇒ 330 degree
Thus, After converting into degree we get;
⇒ 11 pi /6 radians = 330 degree
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In September 2011, Gallup surveyed 1,004 American adults and asked them whether they blamed Barack Obama a great deal, a moderate amount, not much, or not at all for U.S. economic problems. The results showed that 53% of respondents blamed Barack Obama a great deal or a moderate amount. Calculate the 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems.
Answer:
The 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is (0.4894, 0.5706)..
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1004, \pi = 0.53[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.53 - 2.575\sqrt{\frac{0.53*0.47}{1004}} = 0.4894[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.53 - 2.575\sqrt{\frac{0.53*0.47}{1004}} = 0.5706[/tex]
The 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is (0.4894, 0.5706)..
The 99% confidence interval for the proportion of American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is approximately 0.502 to 0.558.
Explanation:To calculate the 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems, we can use the formula:
CI = p ± Z * sqrt((p * (1-p)) / n)
Where:
CI = Confidence interval
p = Proportion of respondents who blamed Barack Obama a great deal or a moderate amount
Z = Z-score corresponding to the desired confidence level
n = Sample size
Given that 53% of respondents blamed Barack Obama a great deal or a moderate amount and the sample size is 1,004, we can calculate the confidence interval as follows:
CI = 0.53 ± Z * sqrt((0.53 * (1-0.53)) / 1004)
Since we want a 99% confidence interval, the corresponding Z-score is 2.58 (obtained from a standard normal distribution table).
Plugging in the values:
CI = 0.53 ± 2.58 * sqrt((0.53 * (1-0.53)) / 1004)
Calculating the standard deviation and rounding to 2 decimal places:
CI = 0.53 ± 2.58 * sqrt(0.53 * 0.47 / 1004)
CI = 0.53 ± 2.58 * sqrt(0.2491 / 1004)
CI = 0.53 ± 2.58 * 0.0157
The 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems is approximately 0.502 to 0.558.
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At what point does the line given by the following equation cross the x-axis?
y = -x + 7
Answer:
(7,0)
Step-by-step explanation:
you can 0 in for Y in order to find the x-axis
0=-x+7
-7=-x
x=7
Answer:
(7, 0)
Step-by-step explanation:
We are trying to find the location that the equation crosses the x-axis.
This location is also known as the x-intercept.
To find the x-intercept, you can just set y in the equation to 0 and then solve for x.
0 = -x + 7
-x = -7
x = 7
So, the x-intercept is 7.
X-intercepts always have a y of 0 by definition, so it can be found at the point (7, 0)
if each slice of pizza is 1/16 of the pizza what is the decimal form of 8 slices of pizza
Answer:
0.5
Step-by-step explanation:
8 slices of a pizza cut into 16 pieces is a half of the pizza. A half is 0.5
What ordered pair corresponds to the vertex of the function
Answer:A+b
by-step explanation:
Answer:
you have the correct answer!
Step-by-step explanation:
What is 11/12 minus 7/9
Answer:
5/36
Step-by-step explanation:
This is in fractions so that's what i did and its simplified as well