The probability that someone who tests negative does not have the disease is 0.8451
Given that,
The information shows the outcomes of a test for a specific illness. Assume a member of the group is chosen at random.
From given data table,
N = 144+ 22 + 14+ 120 = 300
n(not disease) = 22 + 120 = 142
n( negative And not disease) = 120
P( Not disease) = 142/300
P( Negative and not disease) = 120/300
Therefore,
P(Negative/ not ..disease) =[tex]\frac{P(Negative and not,.disease)}{P(Not ,.disease)}[/tex]
=[tex]\frac{120/300}{142/300}[/tex]
=[tex]\frac{120}{142}[/tex]
=0.8451
Hence, The probability approximately is 0.8451
Hence, the probability that someone who tests negative does not have the disease is 0.8451
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what is the answer to 2 (x + 14)=90
Answer:
x = 31
Step-by-step explanation:
Distribute 2 to x which equals 2x, and 2 times 14 which equals 28, which gets you to 2x + 28 = 90, then subtract 28 from 90, which leads you to
2x =62, and the final step is to divide 2 from 62 which gets you 31.
Last year students planted 8 tomato plants and 16 pepper plants in a school garden
Answer:
whats the question
Answer:
What are you asking?
Enter the equivalent decimal.
9/9/25
Answer:
Step-by-step explanation:
.36
how can i tell if an equation is linear/non linear without using a graph?
Answer:
Using an Equation
Simplify the equation as closely as possible to the form of y = mx + b. Check to see if your equation has exponents. If it has exponents, it is nonlinear. If your equation has no exponents, it is linear.
Answer:
Step-by-step explanation:
To be linear it must have the form y=mx+b.IN a linear equation the variables are shown in first degree and terms with products of variables are absent .
what is the product of 5/6 x 4 2/3
Answer:
35/9
Step-by-step explanation:
What fraction is a hour in 20 mins
20 minutes is [tex]1/3^{rd}[/tex] of an hour
PLEASE HELP ME ASAP !!!!!!!!!!!!!!!!!!!
The triangles in the diagram indicates that ΔABD is an isosceles triangle, therefore;∠2 ≅ ∠1
The two-column method can be used to prove that the angle m∠BAC > m∠C as follows;
Statement [tex]{}[/tex] Reasons
1. BC > BA [tex]{}[/tex] 1. Given
2. BA ≅ BD [tex]{}[/tex] 2. Given
3. ΔABD is an isosceles Δ[tex]{}[/tex] 3. Definition of isosceles triangle
4. ∠1 ≅ ∠2 [tex]{}[/tex] 4. Base ∠s of isosceles triangle ΔABD
5. ∠1 = ∠2 [tex]{}[/tex] 5. Definition of congruency
6. ∠1 = ∠3 + ∠C [tex]{}[/tex] 6. Exterior angle theorem
7. ∠2 = ∠3 + ∠C [tex]{}[/tex] 7. Substitution property
8. ∠2 - ∠3 = ∠C [tex]{}[/tex] 8. Subtraction property
9. ∠2 > ∠C [tex]{}[/tex] 9. Definition
What is an isosceles triangle?An isosceles triangle is a triangle that have a pair of congruent sides and one pair of congruent angles.
The reasons in the above two-columns used to prove m∠BAC > m∠C are as follows;
Isosceles triangle ΔABD
The triangle ΔABD that have side AB congruent to side BD is an isosceles triangle by definition of an isosceles triangle.
The base angles of an isosceles triangle that are angles opposite congruent sides in a triangle are also congruent.
Definition of congruency
A geometric figure is congruent to another figure if their measurements are the same.
Exterior angle theorem
The exterior angle of a triangle theorem states that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.
Substitution property
The substitution property of equality states that if a quantity a is equal to another quantity b then a can be substituted by b in expressions and equations without changing their value.
Subtraction property
The subtraction property of equality states that if the same quantity is subtracted from both sides of an equation, then the new amount obtained are also equal
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PLS HELP ASAP!!!!!! 100 PTS ANSWER BOTH REASON 6 AND 7! ALL CHOICES ARE THE SAME
Answer:
CPCTC
Step-by-step explanation:
BD is perpendicular to AC, forming two right triangles. The hypotenuses are congruent, as is our leg that we will call b. If we use Law of Sines to find our angles a and c (no matter the values), we would find that because b is the same leg in both triangles and the hypotenuses are congruent, angles a and c are congruent, so therefore your missing angle in both triangles is congruent, and using a trig function will find that AD and CD are congruent, making all of both triangles congruent.
A flagpole casts a 20-foot shadow at the
same time Lexi casts a 5-foot shadow. If
Lexi is 5'9", find the height of the flagpole.
Answer:
20-foot shadow
Step-by-step explanation:
For daniel's lemonade recipe, 4 lemons are required to make 16 cups of lemonade. At what rate are lemons being used in lemons per cup of lemonade?.
Using mathematical operations we can conclude that the rate of lemons being used in a cup of lemonade is 1/4.
What are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."
The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.
In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
So, we know that:
Lemons required to make 16 cups of lemonade: 4 lemons
Then, the rate of lemons being used in lemonade per cup:
4/16
1/4
Therefore, using mathematical operations we can conclude that the rate of lemons being used in a cup of lemonade is 1/4.
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find the open intervals on which the function f(x)axbxc, a0, is increasing and decreasing. describe the reasoning behind your answer.
The intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing is x>-b/2a and x<-b/2a
Given that,
We have to find the intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing.
We know that,
Take the function equation,
f(x)=ax² + bx + c
The derivative of the function of x is
f'(x)=ax+b
So, f(x) is increasing when f'(x) > 0
f(x) is decreasing when f'(x) < 0
Then we can say
f'(x) > 0 , when b > 0 and a < 0
2ax + b < 0
2ax < - b
x<-b/2a
Now,
f'(x) < 0 , when b < 0 and a > 0
2ax + b > 0
2ax > - b
x>-b/2a
Therefore, the intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing is x>-b/2a and x<-b/2a.
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alice and bob are playing a game in which there are several rounds and each round can be a win, a loss, or a draw for alice. if they play 6 rounds, in how many ways can alice win or draw exactly three times? (answer: 300)
AS per the permutation concept, the number of ways can Alice win or draw exactly three times is 240
Permutation:
In probability, permutation refers the arrangement of objects in a definite order.
Given,
Alice and Bob are playing a game in which there are several rounds and each round can be a win, a loss, or a draw for Alice.
Here we need to find the number of ways can Alice win or draw exactly three times, if they play 6 rounds.
While we looking into the given question, we know that,
Total number of games = 6
Possible values = 3 ( win, loss, or draw)
Here we need to find the probability of winning 3 times, it can be calculated by using the permutation as,
=> 6! / (6 - 3)!
=> 6! / 3!
=> 120
Similarly, the the probability of draw 3 times, it can be calculated by using the permutation as,
=> 6!/ (6 - 3)!
=> 120
So, the number of ways can Alice win or draw exactly three times is
=> 120 + 120 = 240
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100 + 100 + 100 + 1000 = X
Answer:
1300=X
Step-by-step explanation:
Answer:
1,300
Step-by-step explanation:
You would first start off with adding 100 + 100= 200. Then you would add another 100 to 200 which is 300. Then comes the final step which is adding 1000 to 300 which = 1300
X= 1,300
Simplify the radical ..... A) √12 B) √50 C)√84 D) √200
Answer:
√12 = 3.46410161514
√50 = 7.07106781187
√84 = 9.16515138991
√200 = 14.1421356237
Step-by-step explanation:
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mr. eaton is ordering sandwiches for a school picnic. the best deal is the 6-foot-long sandwich, which is cut into 4-inch-long pieces. mr. eaton expects 90 people to attend the picnic. he thinks each person will eat 2 pieces. how many 6-foot-long sandwiches should he order?
He should order 10 sandwiches of 6 foot long so, as to make sure that everyone will eat 2 pieces.
What is Conversion ?We need to convert between the units in order to ensure the accuracy and to prevent measurement misinterpretation. For example, we do not measure the pencil's length in kilometres. In this situation, one must convert from kilometres (km) to centimetres (cm) (cm). In most cases, multiplicative conversion factors are used to convert one unit to another of the same quantity. Let's see how to change the length and mass units.
1 Feet = 12 Inches
So, 6 Foot = 72 inches
The Length of sandwich- piece is 4 inch
So, when we convert 6 foot long sandwich into 4 inch,
Then we get number of piece is = 72/4 = 18
From 6 foot long sandwich we get 18 pieces of 4 inch long sub.
Now, Total people who will attend picnic is 40
and each people will eat 2 pieces.
It means total number of piece required = 2 (90) = 180
Mr. eaton required 180 pieces of sandwiches.
Number of sandwiches = 180 / 1.8 = 10
He should order 10 sandwiches of 6 foot long.
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A company produce two type of olar panel per year: x thouand of type A and y thouand of type B. The revenue and cot equation, in million of dollar, for the year are given a follow. R(x,y)=4x5y C(x,y)=x^2-3xy7y^23x-22y-4 Determine how many of each type of olar panel hould be produced per year to maximize profit
Using partial derivatives, we know that in order to optimize profit, the company should produce 7,000 type A solar panels and 8,000 type B solar panels annually.
What are partial derivatives?A function of two or more variables can yield partial derivatives.
Writing the derivative with regard to x while treating all other variables as constants allows one to determine the partial derivative of a function with respect to one variable, let's say x.
The partial derivatives for each of the other
So, for a business making two different types of solar panels, the revenue and cost functions are provided by:
[tex]\begin{aligned}&R(x, y)=4 x+2 y \\&C(x, y)=x^2-4 x y+9 y^2+22 x-114 y-5\end{aligned}[/tex]
If revenue and cost are stated in millions of dollars annually, x represents the thousands of type A solar panels produced and sold annually, and y represents the thousands of type B solar panels produced and sold annually.
By deducting costs from revenues, the profit function is obtained as follows:
[tex]\begin{aligned}&P(x, y)=R(x, y)-C(x, y) \\&P(x, y)=4 x+2 y-\left(x^2-4 x y+9 y^2+22 x-114 y-5\right) \\&P(x, y)=-x^2-9 y^2-18 x+116 y+4 x y+5\end{aligned}[/tex]
The profit function's partial derivatives with regard to x and y are as follows:
[tex]\begin{aligned}&\frac{\partial P}{\partial x}=-2 x+4 y-18 \\&\frac{\partial P}{\partial y}=4 x-18 y+116\end{aligned}[/tex]
When both of these partial derivatives are equal to zero, the profit is maximized:
[tex]\begin{aligned}&0=-2 x+4 y-18 \\&0=4 x-18 y+116\end{aligned}[/tex]
The first equation above is multiplied by two, and the two equations are then added to yield:
[tex]\begin{aligned}&0=-10 y+80 \\&y=8\end{aligned}[/tex]
Inputting into the first equation results in:
[tex]\begin{aligned}&0=-2 x+4(8)-18 \\&2 x=14 \\&x=7\end{aligned}[/tex]
Therefore, using partial derivatives, we know that in order to optimize profit, the company should produce 7,000 type A solar panels and 8,000 type B solar panels annually.
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a stone is tossed into a lake, sending out circular ripples whose area is increasing at the rate of 520 ft2/sec. how fast is the radius increasing when the radius is 30 feet?
The radius is increasing fastly at a rate of 2.75 feet per second when it is already 30 feet.
Here, it has been told that the rate of change of the area with respect to the time is = 520 ft²/sec - (i)
This can also be written as = dA/dt (ii)
We need to find the rate of change of radius with respect to the time at 30 feet. This can be written as = dr/dt (iii)
We already know that the area of a circle can be found out using the formula = πr² (iv)
Differentiating equation (ii) with respect to time, we get -
= d(πr² )/dt
= π*(dr²/dt)
= π*(dr²/dr)*(dr/dt)
= π*(2r)*(dr/dt)
= dr/dt = (dA/dt)*(1/ π*2r)
Using the given values, we get -
= (dr/dt) = 520 / π*2*30ft
= (dr/dt) = 2.75 ft/sec
Henceforth, we find that the rate of change of the radius with respect to time at 30 feet is going to be 2.75 ft/sec.
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the given pattern continues. write down the nth term of the sequence suggested by the pattern 1/18, 2/19, 3/20, 4/21
The nth term of the pattern is (1+n)/(18+n)
What is a sequence?
succession is the act of doing something after another. successional order: a list of books organized by title. a running or interconnected sequence: a series of sonnets. something that happens after; a following event; a result; or a repercussion. In contrast to a set, the order of the components in a sequence does important, and the same elements may occur more than once at various positions. A series can officially be described as a function from natural numbers.
We are given a sequence
1/18, 2/19, 3/20, 4/21
As we can see the second term is (1+1)/(18+1)
Third term is (1+2)/(18+2)
Hence the n th term of the sequence can be given as (1+n)/(18+n)
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Solve negative 5 times y plus seven thirds times y equals negative 5 minus eight thirds times y minus 4 for y.
Infinite solutions
No solution
y = −14
y = 0
NEED A ANSWER ASAP!!!!!!!
Answer:
None of the Above?
Step-by-step explanation:
1.) If we put this into words, we would get -5y+7/3y=-5-8/3y-4
2.) By moving all y terms to one side, we get -5y + 7/3y + 8/3y = -5 - 4
3.) By simplifying, you would get -4 2/3y = -9.
4.) If you divide both sides by -4 2/3, you would get that y = -9 * - 3/14 = 27/14
Which angle is an adjacent interior angle to ∠jkm? ∠jkl ∠mkl ∠klm ∠lmk
∠mkj angle is an adjacent interior angle to ∠jkm
Adjacent interior angles are two angles that share a common vertex and a common side. In the given angle ∠jkm, the common vertex is at point "k" and the common side is the line segment joining points "j" and "m". Therefore, the adjacent interior angle to ∠jkm is ∠mkj.
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What value does each equation need to be multiplied by in order to eliminate the x-terms?
Equation 1: 6x − 5y = -4
Equation 2: 4x + 2y = 28
Please help
You need to find what x is equal to for each equation, so you can sub why x is equal to in the place I'd x to eliminate the variable
1. 6x-5y=-4
6x=5y-4
X=5/6y-2/3
2. 4x+2y=28
4x=-2y+28
X=-1/2y+7
Hope this helps!
What are the prime factors of 48?
Answer:
48 = 2⁴ · 3
Step-by-step explanation:
You want the prime factorization of 48.
Prime factorsYou recognize that 48 is an even number, so you can divide by 2 and see what's left. You can keep doing that until you get a number divisible by another prime:
48/2 = 24
24/2 = 12
12/2 = 6
6/2 = 3
3 is prime.
The prime factorization of 48 is ...
48 = 2⁴ · 3
Carlos wants to buy some new video games. Each game he buys costs him $36. Is the relationship between the number of games Carlos buys and the total price proportional?
The relationship between the number of games Carlos buys and the total price is proportional.
What is a proportional relationship?
A proportional relationship exists between two or more variables if they move in the same direction. If one of the variables increases, the other variable increases.
As the number of games that are bought increases, the total price paid also increases. This means that the relationship is proportional.
The formula that is used to represent proportional relationship is:
T = kg
Where:
T = total price k = constant g = number of games boughtT = $36g
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guillermo bought textbooks and notebooks at the bookstore . the number of textbooks was three more than twice the number of notebook .he hought seven textbooks . how many notebooks did he buy?
2 notebooks
Step-by-step explanation:
the variables I'm gonna use are t for textbooks and n for notebooks
t = (n•2)+3 (two times the notebooks then add 3)
now we'll plug in the amount of notebooks we have so t=7
7=(n•2)+3
we can subtract 3 from each side that leaves us with
4=n•2
then divide by 2
2=n
Guillermo bought 2 notebooks
Please find out the slope and the y-intercept and put it in the y=mx+b
Answer:
y = [tex]\frac{3}{4}[/tex]x + 2
Step-by-step explanation:
To find the slope we will use the slope formula of y2-y1/x2-x1.
Our two y values are 2 and -1.
Our two x values are 0 and 4.
2 - (-1) = 3
0 - 4 = -4
3/4 = [tex]\frac{3}{4}[/tex]
y = [tex]\frac{3}{4}[/tex]x + 2
jacob is an american, has been a smoker since he was 21, and is now 48 years old. if he continues to smoke, his smoking habit might shorten his life expectancy by an average of how many years?
Jacob's smoking habit may shorten his life expectancy by an average of 10 years and 6 months.
Given,
The age of Jacob when he starts smoking = 21 years
Jacob's present age = 48 years
In generally if 1 year of smoking reduces 6 months from the life.
Why does smoking cause life to be shorter?
Only a few of the illnesses that are directly linked to smoking and have a significant role in the increased mortality rate among smokers include cancer, lung disease, and cardiovascular disease. The link between smokeless tobacco and cancer is well known.
Here,
Jacob may live 10 years and 6 months less than normal due to his smoking habit.
I have answered the question in general as given question is incomplete.
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In VWX, X ≈ W, WX = 17 and VW = 16. Find XV. HELPPPPP
Answer:
XV = 16
Step-by-step explanation:
Triangle VWX is an isosceles triangle. Since the base angles are the same, the sides opposite the angle are also the same. See image. They gave VW so XV is the same as VW.
1. Malik wants to buy his brother a hover board for his birthday.
He was hoping to spend only $150 total on his gift. Target was
having a 20% off sale on their hoverboards. Can Malik afford
the hoverboard with the discount?
Using percentage formula, Malik can afford the board with the discount only if he has $120 with him
PercentageA percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
To know if Malik can afford the hoverboard, we have to calculate 20% of 150
20% of 150 = 20/100 = x /150
0.2 = x / 150
x = 150 * 0.2
x = 30
Subtracting the discount, the amount will be 150 - 30 = 120
Malik can afford the hoverboard if he has $120 with him.
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suppose that based on a random sample, a 95% confidence interval for the mean hours slept (per day) among graduate students was found to be (6.5, 6.9). what is the margin of error of this confidence interval? responses
The margin of error for the confidence interval (6.5, 6.9) is 0.2 , the correct option is (c) .
In the question ,
it is given that ,
the 95% confidence interval for mean hours slept in the graduate students is (6.5, 6.9) ,
we have to find the margin of error ,
we know that the formula for the margin of error is
= (upper limit of confidence interval - lower limit )/2
From the given interval ,
we see that ,
upper limit of confidence interval = 6.9
lower limit of confidence interval = 6.5
Substituting the above value in margin of error formula ,
we get ,
margin of error = (6.9 - 6.5)/2
= 0.4/2
= 0.2
Therefore , the margin of error is 0.2 .
The given question is incomplete , the complete question is
Suppose that based on a random sample, a 95% confidence interval for the mean hours slept (per day) among graduate students was found to be (6.5, 6.9). What is the margin of error of this confidence interval? responses
(a) 6.7
(b) 0.4
(c) 0.2
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Peter opened up a savings account by making an initial deposit. After the initial deposit, Peter has been adding
$50 to his savings account each month. If after 8 months Peter has a total of $600 in his savings account, what
was the amount of his initial deposit?
Answer:
$200
Step-by-step explanation:
so if peter has been depositing 50 each month for 8 months then you would just do 50x8 which equals 400 and 600-400=200