The probability that a woman has a malignant tumor in her breast is 7.5%. ie 75
Let + = mammogram result is positive
B = tumor is benign
M = tumor is malignant.
Note that Bc = M.
given that P(M) = .01,
so P(B) = 1 − P(M) = 0.99.
We are also given the conditional probabilities
P(+ | M) = .80 and
P(− | B) = .90, where the event − is the complement of +
P(+ | B) = .10
Bayes’ formula:-
P(M | +) = P(+ | M) P(M) / (P(+ | M)P(M) + P(+ | B)P(B))
= 0.80 × 0.01 / (0.80 × 0.01 + 0.10 × 0.99)
=0.075
So the chance would be 7.5%. ie 75
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Phil lives in a state where his tax rate does not change when his income changes. This is an example of a(n) ____ ?
Phil lives in a state where his tax rate does not change when his income changes. This is an example of a proportional or flat tax.
What is tax?Tax is defined as the official way individuals contribute to their state revenue through the compulsory deduction of some amount of money from their monthly income.
There are two types of tax which include the following:
Regressive tax,Progressive tax, andProportional or flat tax.Proportional or flat tax: This is defined as the type of tax that is being paid by individuals from different class in the society whereby all are expected to pay tax with the same rate irrespective of the income.
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A cat’s heart beats approximately 45 times in 15 seconds. At this rate how many times does the cat′s heart beat per second?
Work Shown:
45 beats = 15 seconds
45/15 beats = 15/15 seconds
3 beats = 1 second
To convert to beats per minute (bpm), multiply by 60.
There are 39 students in the bike club.
All but 8 of them participated in a race.
What is the total cost if each student who entered the race paid $6?
Answer:
Total Cost = $186
Step-by-step explanation:
All but 8 means that All of them participated except for 8 of them
Since there is 39 Students in the Club
Then the Number of Students participated = 39 - 8 = 31 Students
Total Cost = (Cost per Student ) * ( Number of Students )
=$6 * 31 = $186
Glad to Help
3. Suppose that your calculator does not have a square root key. How could you still use your calculator to determine √144?
Answer
12
Step-by-step explanation:
click on square root
click on 144
then your answer will pop out below your equation
48) in how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people, if a) the bride must be in the picture?
The number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.
What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]
Given, 6 people are to be selected from a group of 10, where the bride must be in the picture.
Following the statements in question, the bride since always there assists for filling five empty spaces using 9 people.
Since five positions are to be filled by nine people, the total number of ways possible = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.
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four vehicles are traversing a 1-km segment of a highway and the following observations are made: vehicle a: 1.2 min vehicle b: 1.5 min vehicle c: 1.7 min vehicle d: 1.4 min what is the space-mean speed?
Using the concept of average speed we conclude that the space-mean speed of the vehicles is 0.69 km/min.
What is space-mean speed?The average speed of a vehicle traveling a given segment of a highway in a specific time period is called space-mean speed, i.e.
Average mean speed = total distance traveled / average time travel
Given for vehicles are traversing a 1 km segment of highway. Hence total distance is 4km.
Average time = (1.2 + 1.5 + 1.7 + 1.4)/4
= 5.8/4
= 1.45 min
Now Average mean speed = 1/1.45
=0.689
=0.69 km/min
Hence the space-mean speed of the vehicles is 0.69 km/min
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TEXT ANSWER
Jason provided the following work when asked to convert 0.105 to its simplest fraction
form.
1. Why did Jason get the problem wrong?
2. Provide the work for properly writing the decimal in its simplest fraction form.
Jason's Work:
0.105=
105
21
1000 200
Answer:
See below
Step-by-step explanation:
.105 is 105 THOUSANDTHS or 105/1000
Divide top and bottom by '5'
to get 21/100
2x+y=4 1x-y=11 adding subtracting equations to solve systems.
By solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3
What is meant by an equation?An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign =. In French, an equation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.
An equation is composed of two expressions joined by an equals sign (=). The expressions on the two sides of the equals sign are referred to as the equation's left-hand side and right-hand side. The right side of an equation is frequently considered to be zero.
Given,
2x+y=4
x-y=1
By solving above two equations we get,
2x+y=4
x-y=1
3x=5
x=5/3
y=-1+x
y=(5/3)-1
y=2/3
Therefore, by solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3
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2– 1 8 y=11+ 7 8 y solve the y
Answer:
y=-3/32
Step-by-step explanation:
2-18y=11+78y
-18y-78y=11-2
-96y=9
y=-3/32
1. Name a plane parallel to plane WXT
2. Name two segments parallel to VU.
3. Name two segments parallel to SW.
4. Name two segments skew to XY.
5. Name two segments skew to VZ.
The plane which is parallel to the line WXT is UVZW
two segments parallel to VU is ST and WX
two segments skew to XY is UT
two segments skew to VZ is YU and TX
What are parallel lines ?Lines that are always the same distance apart in a plane are said to be parallel. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.
Given : The quadrilateral prism
Parallel lines means lines which does not interact and run parallel meaning they have equal distance between them.
The plane which is parallel to the line WXT is UVZW
two segments parallel to VU is ST and WX
two segments skew to XY is UT
two segments skew to VZ is YU and TX
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Can anyone state the vertex of the graph?
There is no vertex in the graph and the transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?The graph represents the given parameter
As a general rule, the maximum or the minimum of a graph is the vertex
In this case, there is no maximum or minimum in the graph
This means that that there is no vertex in the graph
The transformationHere, we have:
We can see that:
The graph is 4 units to the left of the origin and 2 units below the origin
This means that the function has been shifted down and shifted to the left
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a random sample of 26 checking accounts at a bank showed an average daily balance of $300 and a standard deviation of $45. the balances of all checking accounts at the bank are normally distributed. develop a 95% confidence interval estimate for the mean of the population.
The confidence interval estimate for the mean of the population at 95% is [$282.70, $317.30].
Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.
CI = μ ± z x (SD / √n)
where CI = confidence interval
μ = sample mean
z = found by using a z-score table
SD = sample standard deviation
n = sample size
At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.
(100 - 95) / 2 = 2.5
100 - 2.5 = 97.5
Find 0.975 in the z-table to get the value of z.
At p = 0.95, z = 1.96
Plug in the values and solve for the confidence interval.
CI = μ ± z x (SD / √n)
CI = 300 ± 1.96 x (45 / √26)
CI = 300 ± 17.30
CI = [$282.70, $317.30]
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Find the slope of the line. Write your answer in simplest form.
HELP ME PLEASEEEEEEEEEEEEEEEEEEEEE
Answer:
0,3
Step-by-step explanation:
it between the 2 and it is negative and positive cases in the -2
- is slightly variable - and follows a nearly normal distribution - with a mean of 25 square feet - and a standard deviation of 3 square feet. (a) what is the probability that - the area covered by a can of spray paint - is more than 27 square feet?
The probability that the area covered by a can of spray paint is 0.251
The variable of interest is:
X: are objects that can be painted with a single can of spray paint.
This variable has a normal distribution, with a mean of 25 feet square and a standard deviation of 3 feet square.
Symbolically:
P(X≥27)
To calculate the probability, use the standard normal distribution, so first standardize the value of X using:
Z= (X-μ)/σ
P(X≥27)= P(Z≥(27-25)/3)= P(Z≥0.67)
Now, because the Z-table contains cumulative probability information:
P(Zα≤Z₀)=1-α
you must perform the following conversion to calculate the requested probability:
1 - P(Z<0.67)= 1 - 0.749= 0.251
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2. Write 420 as a product of prime numbers.
Answer:
As a product of prime numbers:
420 = 2 × 2 × 3 × 5 × 7
Consider the quadratic equation.
X^2 -5x=6
If a student wants to factor this equation by the method of completing the square, why term should the student add to both sides as the first steps?
In completing the square method, considering the equation X^2 - 5x = 6 the student should add 25 / 4 to both sides of the equation
How to know term should the student add to both sidesThe quadratic equation is an equation of the form
ax^2 + bx + c
The completing the square method is on of the methods of solving equations of the form above
The factor to be added on the both sides of the equation while using the completing the square method is
(b / 2a)^2
compared to the equation in the problem X^2 - 5x = 6 it is
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The vertex of the graph is (-2, 2), the axis of symmetry of parabola is -2 and the parabola opens downwards.
In the given question we have to find the vertex, axis of symmetry and whether the parabola opens upwards and downwards.
Firstly we find ing the vertex of the graph.
As we know that vertex is the highest and lowest point of the graph.
From the graph the highest point is (-2, 2).
So the vertex of the graph is (-2, 2).
As we know that the axis of symmetry always passes through the vertex of parabola. The x coordinate of the vertex of parabola is the axis of symmetry of parabola.
So the axis of symmetry of parabola is -2.
As we can see that the parabola opens downwards.
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There are 1,459 children registered for camp. There is enough room for 18 campers to sleep in
each cabin. What is the least number of cabins needed for all the registered campers?
Answer:
82 rooms
Step-by-step explanation:
1459/18=81.05
so 82 rooms
Please mark as brainliest
Answer:
82
Step-by-step explanation:
1459/18
[tex]1459 \div 18[/tex]
for each cabin there 18 And there are 1459
81.05 \times 48=159
since you can't have a half a cabinet the answer is 82
A rectangular book measures 3*5. What is the length of its diagonal to the nearest tenth?
The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
Area of rectangle = length × width.
The angle between any two consecutive sides will be 90 degrees.
As per the given rectangle with dimensions 3 × 5.
The rectangle has been attached below,
The length of the diagonal using Pythagoras' theorem is,
x = √(3² + 5²)
x = √34 = 5.8
Hence "The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8".
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Which of the following sets is equal to {1, 2, 3, ...}?
The set which is equivalent and equal to the given set; {1, 2, 3, ...} is; Z+.
Which set is equivalent to the given set?It follows from the task content that the set which is equivalent to the given set; {1, 2, 3, ...} is to be determined.
Since the numbers in the set are all integers and which happen to be positive integers.
Hence, the best representation of a set which is equivalent to the given set as given in the task content is; Z+.
The set of positive integers is represented as Z+. It implies all the integers greater than 0.
Hence, the set which is equivalent to the given set; {1, 2, 3, ...} is; Z+.
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john wanted a pressure washer for a flat fee of $50 plus $9 per hour how many hours did he rent the pressure washer if the total bill was $86?
He rented the pressure washer for 4 hours, given that the total bill was $86.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
Let x = total number of hours he rented the pressure washer
The total bill, which was $86, includes the flat fee of $50 plus $9 per hour of use.
Hence, the equation will be 50 + 9x = 86.
Solve for x.
50 + 9x = 86
9x = 86 - 50
9x = 36
x = 4
total number of hours he rented the pressure washer = 4
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Two complementary angles have measures of x and y. If y is 9 less than twice x, write a system of linear equations that can be used to determine the measure of each angle. Find the measure of each angle.
Using system of linear equation, the complementary angles (x, y) are 27 and 63 degrees respectively.
Complementary AnglesWhen the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles. However, when the sum of the two angles is equal to 180 degrees, the angles are supplementary angles
In this case, we have two angles x, y which are complimentary to one another.
We can represent this with system of equations;
x + y = 90 ...eq(i)y - 9 = 2x ... eq(ii)solving equation (i) and (ii)
The value of x and y are 27 and 63
The complementary angles are 27 and 63
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it is claimed that the mean age of bus drivers in chicago is 50.2 years. if a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
The null hypothesis is a statement which describe the claim of 'no difference'.
Let μ be the population mean.
Given claim : The mean age of bus drivers in Chicago is 50.2 years.
i.e. μ = 50.2
Since "no difference with mean" or statements with an equal sign are used as the null hypothesis.
Then, the null hypothesis for the given situation is
Ηο : μ = 50.2
If the test fails to reject the null hypothesis, it means there is evidence to support the claim that the the mean age of bus drivers in Chicago is 50.2 years.
A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided data. Using sample data, hypothesis testing is performed to evaluate a theory' veracity. It is often referred to as just "the null," and its symbol is Hο.
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g(a)=3a+2; find g(-3) HELP PLEASE!!
The output value of g( -3 ) in the function g( a ) = 3a + 2 is -7.
What is the output value of g( -3 ) in the given function?A function is simply a relationship that maps one input to one output. For relation to qualify as a function, each x-value can only have one y-value.
Given the data in the question;
g( a ) = 3a + 2g( -3 ) = ?To determine the output value of g( -3 ), replace all the occurrence of 'a' with -3 in the function and simplify.
g( a ) = 3a + 2
g( -3 ) = 3( -3 ) + 2
Multiply 3 and -3
g( -3 ) = -9 + 2
Add -9 and 2
g( -3 ) = -7
Therefore, the output value is -7, this forms an ordered pair of (-3,-7).
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Find the slope and the y-Intercept of the line.
-5x + 4y = -3
Write
your answers in simplest form.
Answer:
slope=5/4 y intercept=-3/4
Step-by-step explanation:
put it into slope intercept form y=5/4x-3/4
pull out 5/4 as slope and -3/4 as y intercept
The equation 2x(x + 8) = 110 represents the area of a rectangle.
Solve the equation. What are the approximate dimensions of the rectangle? Express your answers as decimals rounded to the nearest tenth.
The rectangle has its dimensions to be 8.8 units by 12.4 units
How to determine the dimensions of the rectangle?From the question, the equation is given as
2x(x + 8) = 110
This equation represents the area of the rectangle
So, we have
2x(x + 8) = 110
Divide by 2
x(x + 8) = 55
Open the brackets
This gives
x² + 8x = 55
Rewrite as
x² + 8x - 55 = 0
Using a graphing calculator, we have the solutions to be
x = -12.4 and x = 4.4
The variable x cannot be negative
So, we have
x = 4.4
In 2x(x + 8) = 110, we have
Length = 2x
Width = x + 8
So, we have
Length = 2 x 4.4
Width = 4.4 + 8
Evaluate
Length = 8.8
Width = 12.4
Hence, the dimensions of the rectangle are 8.8 units by 12.4 units
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Question 3(Multiple Choice Worth 6 points)
(02.07 MC)
What are the solutions of 2x² + 3x= -8?
The solutions to the equation [tex]2x^{2} +3x=-8\\[/tex] are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex] respectively.
What is a quadratic equation?
A second-degree algebraic equation is a quadratic equation in x.
[tex]ax^{2} +bx+c=0[/tex] is the quadratic equation in standard form, where a and b are the coefficients, x is the variable, and c is the constant term.
To find the root value of x, [tex]x= \frac{-b}{2a}[/tex] ± [tex]\frac{\sqrt{b^{2} -4ac} }{2a}[/tex]
Given, [tex]2x^{2} +3x=-8\\[/tex]
or, [tex]2x^{2} +3x+8=0[/tex]
Comparing the equation [tex]2x^{2} +3x+8=0[/tex] with the equation [tex]ax^{2} +bx+c=0[/tex] , we get
[tex]a=2, b=3, c=8[/tex]
Then, [tex]x= \frac{-3}{2*2}[/tex] ± [tex]\frac{\sqrt{3^{2} -4*2*8} }{2*2}[/tex]
or, [tex]x= \frac{-3}{4}[/tex] ± [tex]\frac{i\sqrt{55} }{4}[/tex]
Taking '+' sign, we get [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex]
Therefore, the solutions of the given equation are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex].
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Write an equivalent ratio for each ratio
Answer:2/5=4/10 and 1/4=2/8
Step-by-step explanation: you can simplify 4/10 to get 2/5 and same with 2/8. You would divide the fraction by two.
Which equation represents the sentence, "The sum of twenty-four and p minus fifteen is q"?
A. 24 + p + 15 = q
B. 24 + p – 15 = q
C. p + q – 15 = 24
D. 15 + p = q – 24
Answer:
B is correct: also if u add C and D together there both different and if u added B and A correctly u would have got B as your answer.
Step-by-step explanation:
Graph the equation by using the slope intercept method
For the given equation 4x + 3y =21 the slope intercept form is given by y = (-4/3)x + 7.
Graph is attached.
As given in the question,
Given equation is equal to :
4x + 3y = 21
To get the slope intercept form of the given equation we have,
Subtract 4x from both the sides of the given equation we have,
4x + 3y - 4x = 21 - 4x
⇒ 3y = 21 - 4x
Now divide by 3 on both the sides of the equation we get,
3y / 3 = (-4/3)x + (21/3)
⇒ y = (-4/3) x + 7
Graph of the given equation in slope intercept form y = (-4/3) x + 7 is attached.
When x = 0 ⇒ y = 7
y= 0 ⇒ x = 21 /4
Therefore, for the given equation 4x + 3y =21 the slope intercept form is given by y = (-4/3)x + 7.
Graph is attached.
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