To solve this problem, we use the formula for binomial probability:
P = [n! / (n – r)! r!] p^r * q^(n – r)
where,
n = total number of adults = 4
r = number of adults who believe in reincarnation = 3
p = chance of believing in reincarnation = 50% = 0.50
q = 1 – p = 0.50
P = [4! / (4 – 3)! 3!] 0.50^3 * 0.50^(4 – 3)
P = 0.25 = 25%
Answer:
Answer is 0.096
Step-by-step explanation:
Here 44 adults are randomly selected.
Each adult selected is independent of the other to believe in reincarnation.
Also there are only two outcomes, probability for success in each trial = 0.50
Hence X no of adults who believe in reincarnation is binomial with n =50 and p = 0.50
[tex]a) P(X=23) = 50C23 (0.5)^{50} =0.096[/tex]
Working notes:
50C23 =108043253365600
0.5^50) = 8.8178x10^(-14)
Simplifying we get answer as 0.096
Find the value of x so that the function has the given value.
r(x)=−5x−1; r(x)=19
x=
To find the value of 'x' that makes the function r(x) = 19, we need to solve the equation -5x - 1 = 19 for 'x'. After doing so, we obtain x = -4.
Explanation:This question involves finding the value of 'x' in a mathematical function provided, in order to get a specific output. The function provided is r(x) = -5x - 1 and the question states that the output r(x) should be 19. We can setup the equation -5x - 1 = 19 and solve for 'x'.
Adding 1 to both sides of the equation, we obtain -5x = 20. Dividing both sides by -5 gives x = -4. So, the value of 'x' that makes the function r(x) = 19 is x = -4.
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Why is x = 4 a solution to the proportion 14/x = 56/16
[tex]\large\text{Hey there!}[/tex]
[tex]\large\text{Step 1: You have to \underline{\bf{CROSS MULTIPLY}}}[/tex]
[tex]\mathsf{\dfrac{14}{x}=\dfrac{56}{16}}\\\\\mathsf{14\times16=56\times x}\\\\\mathsf{14(16)= \ \bf{\underline{224}}}\\\\\mathsf{56(x)=\underline{\bf{56x}}}[/tex]
[tex]\huge\text{We get: \bf{\underline{224 = 56x}}}[/tex]
[tex]\large\text{Step 2: }\large\text{\bf{\underline{FLIP}}}\large\text{ the new equation around}[/tex]
[tex]\huge\text{\bf{\underline{56x = 224}}}[/tex]
[tex]\large\text{Step 3: \bf{\underline{DIVIDE}}}\large\text{ both of your sides by 56}[/tex]
[tex]\mathsf{\dfrac{56x}{56}=\dfrac{224}{56}}\\\\\mathsf{Cancel\ out: \dfrac{56x}{56}\ because\ that\ gives\ us\ 1}\\\\\mathsf{Keep: \dfrac{224}{56}\ because\ it\ gives you\ the\ value\ of\ x }\\\\\mathsf{\dfrac{224}{56}=4}\\\\\mathsf{x=4}[/tex]
[tex]\boxed{\large\text{So, the reason why x = 4 for this equation is because } \mathsf{\dfrac{14}{4}}\ \& \ \dfrac{56}{16}\ \large\text{ are equal to each}}\\\boxed{\large\text{other. }}[/tex]
[tex]\mathsf{\dfrac{14}{4} = 3.5}[/tex]
[tex]\mathsf{\dfrac{56}{16} = 3.5}[/tex]
[tex]\huge\text{\bf{3.5 = 3.5}} \ \checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\dag\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
Find the dimensions of the rectangular corral split into two pens (sharing a fence) of the same size producing the greatest enclosed area given 630 630 feet of fencing.
To find the dimensions of the rectangular corral split into two pens that produce the greatest enclosed area, use the perimeter and area formulas for a rectangle.
Explanation:To find the dimensions of the rectangular corral split into two pens that produce the greatest enclosed area, we can use the perimeter formula for a rectangle. Let L and W represent the length and width of each pen. The total fencing length will be 2L + 3W, and since it is given as 630 feet, we have 2L + 3W = 630. We can rearrange this equation to solve for one variable in terms of the other, substitute it into the area formula for a rectangle, and then find the maximum value using the first derivative test.
Using the equation 2L + 3W = 630, we can solve for L in terms of W: L = (630 - 3W) / 2. Substituting this into the area formula A = LW, we get A = (630 - 3W)W / 2. Taking the first derivative of A with respect to W, we have dA/dW = 630/2 - 3W/2. Setting this equal to zero, we find W = 105. Substituting this back into the equation 2L + 3W = 630, we can solve for L: 2L + 3(105) = 630, and simplifying gives L = 210/2 = 105.
Therefore, the dimensions of each pen that produce the greatest enclosed area are 105 feet by 105 feet.
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If you drive at 100km/hr for 6 hours, how far will you go
The distance covered by the vehicle in 6 hours will be 600 km.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
If you drive at 100km/hr for 6 hours.
Then the distance covered by the vehicle in 6 hours will be given as,
100 = Distance / 6
Distance = 100 x 6
Distance = 600 km
The distance covered by the vehicle in 6 hours will be 600 km.
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100/225 square feet of your bakery will be used as your storefront, where customers come to visit. the rest will be for storage and baking. In simplest form, what fraction of the space will be for storage and baking?
Someone's work
(225-110)/225
125/225
5/9
how did you get (225-110)? if it's 100/225
Answer: 5/9 will be the fraction of the space will be for storage and baking.
Step-by-step explanation:
Since area of bakery will be used as our storefront, where customers come to visit= 100/225
Thus, the total area of bakery = 225
And, the area will be used our storefront, where customers come to visit= 100
So, the remaining area which is used for storage and baking = 225 - 100 =125
So the part of area which is used for storage and baking= the remaining area which is used for storage and baking/ total area
=125/225= 5/9
which is the simplest form.
Assume ABC DEF. If AB = 12, BC = 15, and AC = 17, what is the length of EF? A. 15 B. 17 C. Cannot be determined D. 10
Answer:
Option A) EF = 15 units.
Step-by-step explanation:
We are given the following information in the question:
ΔABC ≅ ΔDEF
AB = 12, BC = 15, and AC = 17
If two triangles are congruent then they have the following properties:
AB = DE
BC = EF
AC = DF
[tex]\angle A = \angle D \\\angle B = \angle E \\\angle C = \angle F[/tex]
Hence, by congruency:
BC = EF
EF = 15 units.
Thus, option A is the correct answer.
What is the length of EF in the right triangle below
The correct answer is 24.
Cole has 67 coins and 23 of them are nickels. 25% of the remaining coins are dimes. How many dimes does Cole have?
Which theorem could kari use to show the measure of angle qml is supplementary to the measure of angle snk? (1 point)?
Is 0.33 bigger than 20/60?
A mixture can be classified as a solution, suspension, or colloid based on _____. its total number of particles
the color of its particles
the scattering of its particles
the size of its particles
What is the equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is 3x + 4y = 15?
Answer: [tex]3x+4y=16[/tex]
Step-by-step explanation:
Given equation of a line = [tex]3x + 4y = 15[/tex]
i.e. [tex]4y = 15-3x[/tex]
i.e. [tex]y=\dfrac{15}{4}-\dfrac{3}{4}x[/tex]
i.e. [tex]y=-\dfrac{3}{4}x+\dfrac{15}{4}[/tex] (1)
It is in intercept form [tex]y=mx+c[/tex] (2) , where m is slope.
By comparing (1) and (2) the slope of line : [tex]m=-\dfrac{3}{4}[/tex]
Also the parallel lines have same slope .
The equation of a line passing through a point (a,b) and having a slope of 'm' is given by :-
[tex](y-b)= m(x-a)[/tex]
Then the equation of the line that passes through (8,-2) and having slope of [tex]m=-\dfrac{3}{4}[/tex] is given by :-
[tex](y-(-2))=- \dfrac{3}{4}(x-8)[/tex]
[tex]4(y+2)=-3(x-8)[/tex]
[tex]4y+8=-3x+24[/tex]
[tex]3x+4y=24-8[/tex]
[tex]3x+4y=16[/tex]
Hence , the equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is [tex]3x + 4y = 15[/tex] is [tex]3x+4y=16[/tex]
.
PLEASE HELP! 10 POINTS!
Which algebraic expression represents the phrase below?
The quotient of the opposite of a number squared and three
*choices below*
Which statement is true about the value of |-5|
A. It is the distance that –5 is from 0 on the number line.
B. It is the distance that –5 is from 5 on the number line.
C. It is less than 5.
D. It is greater than 5.
Mrs garcia is is 1 year less than 3 times as old as her daughter. seven years from now, she will be 4 years more than twice as old as her daughter will be then
A deli offers a choice of 3 breads, 4 meats, and 7 toppings. Using these ingredients, how many possible sandwich combinations are there?
Answer:
3*4*7
Step-by-step explanation:
There is total of 84 combinations
Find the second and third term of the arithmetic sequence -7, _, _, -22, -27, ...
A. -12, -15
B, -17, -12
C. -10, -17
D. -12, -17
Final answer:
The second and third terms of the arithmetic sequence are -12 and -17, found by adding the common difference of 5 to each succeeding term in the sequence.
Explanation:
The question is asking to find the second and third terms of an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which the difference between the consecutive terms is constant. This constant difference is known as the common difference. In the given arithmetic sequence (-7, _, _, -22, -27), we can find the common difference by subtracting two successive terms. For this sequence, the difference between -27 and -22 is -27 - (-22) = -27 + 22 = -5. This implies that to find the previous terms, we should add 5 to each term going backwards.
Starting with -22 and adding 5, we get -17 for the third term. Similarly, adding 5 again for the second term, we get -12. Therefore, the second and third terms of the arithmetic sequence are -12 and -17, respectively.
Will a negative number become positive when exponent is positive fraction
What is the length of leg s of the triangle below
Answer: The correct option is (B) 3.
Step-by-step explanation: We are given to find the length of the leg s in the triangle shown in the figure.
From the figure, we note that
the given triangle is a right-angled one, where
length of the hypotenuse, h = √18 units,
length of one leg, p = 3 units
and
length of the other leg, s = ?.
From Pythagoras theorem, we have
[tex]h^2=p^2+s^2\\\\\Rightarrow (\sqrt{18})^2=3^2+s^2\\\\\Rightarrow 18=9+s^2\\\\\Rightarrow s^2=18-9\\\\\Rightarrow s^2=9\\\\\Rightarrow s=3.[/tex]
Thus, the length of the leg s is 3 units.
Option (B) is CORRECT.
Someone please help me ?
The posted speed limit is 55 MPH. If you’re driving 1000 feet per minute, are you going too fast?
Paige made $1411.75 last year by investing a total of $15,250 in two accounts: one paying 8.5% annual interest and the other paying 10% annual interest. How much did she invest in each account?
When making bread from scratch, the recipe calls for 2/4 cup of water. If you need to make a smaller portion of the recipe, how much water would you need in order to make only 1/6 of the recipe? Give your answer as a fraction, reduced to lowest terms
You would need 1/12 cups of water in order to make only 1/6 of the recipe
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
What are Arithmetic operations?Arithmetic operations can also be specified by addition, subtraction, dividing, and multiplying built-in functions.
When making bread from scratch, the recipe calls for 2/4 cup of water. If you need to make a smaller portion of the recipe,
If a recipe requires 2/4 cup of water, then a fraction of the recipe requires 1/6 cup of water.
So the fraction of the recipe requires 1/6 cup of water as
⇒ 1/6×2/4
⇒ 2/24
⇒ 1/12
Hence, you would need 1/12 cups of water in order to make only 1/6 of the recipe.
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How to determine if two functions are inverses?
Final answer:
Two functions are inverses if, when composed, they return the original input value (identity function). For example, an exponential function and its inverse, the natural log, undo each other. This can be checked with the equations by rearranging and setting equal to isolate constants or applying the functions one after the other.
Explanation:
How to Determine if Two Functions Are Inverses
To determine if two functions, F and G, are inverses of each other, you can compose the functions and see if the result is the identity function. The composition of two inverse functions will output the original input value, meaning that if you take a value x, apply function F to get F(x), and then apply function G to this result, i.e., G(F(x)), you should get x back if F and G are true inverses. The same must hold true in the reverse order, where G is applied first, followed by F: F(G(x)) = x.
To illustrate this concept, let's consider the exponential function and its inverse function, the natural log.Exponential functions are undone by their inverses, natural logs, according to the relation[tex]eln(x) = ln(ex)[/tex]to see this is with the equations involving a constant A, for instance, these can be rearranged to isolate ln A and set them equal to obtain an identity.
Another familiar context is the square and square root functions. To "undo" a square, you take the square root and vice versa. This "undoing" operation is a key characteristic of inverse functions.
Remember that not all functions have inverses, only those that are one-to-one, meaning for each x there is a unique y and vice versa, have inverses that can be defined over their entire domain.
Suppose p = log n ( g ) p=logn(g). define an exponential relationship between p , n , p,n, and g g.
How to find the square root of an improper fraction?
To find the square root of an improper fraction, simplify the fraction if possible, convert it into perfect squares, or use the properties of exponents. If it is already in simple form like 49/100, directly find the square roots of the numerator and denominator separately. Otherwise, use multiplication to manipulate the fraction into a more manageable form for taking square roots.
To find the square root of an improper fraction, the process involves several steps, similar to finding the square root of any number. First, simplify the fraction if possible. In some cases, this may involve multiplying the numerator and denominator by the same factor to make the radical easier to simplify. For instance, if you have an improper fraction like 49/100, you can easily identify that both the numerator and the denominator are square numbers. So, the square root of 49/100 equals the square root of 49 divided by the square root of 100, which simplifies to 7/10.
When the fraction cannot be simplified easily, a different approach is by converting the numerator and denominator into perfect squares, simplifying the expression within the radical, or using properties of exponents to re-express the square root. For example, if you have a fraction like 1/2, you can multiply both the numerator and denominator by 2 to get 2/4. Then you would rewrite the square root as the square root of 2 over the square root of 4, which simplifies to the square root of 2 over 2.
Martin has 4 tickets to ICe Fantasy with the Stars. They cost him $15.75 each, plus $3.50 in handling per ticket, and $9.50 in shipping. What was the total cost of the tickets?
86.50
79.50
70.00
99.50
Through: (-4,4), perp. To y=4/5x-1
True or false? To begin an indirect proof, you assume the converse of what you intend to prove is true.
A. True
B. False
Answer:
The statement is false.
Step-by-step explanation:
To begin an indirect proof, you assume the converse of what you intend to prove is true. This is false.
Rather the correct answer is that to begin an indirect proof, you assume the inverse of what you intend to prove is true.
The converse can be either true or false, depending on what the original statement is, so assuming the converse is pointless.
I have a right triangle they need an equation from me.the truangle is X,4,7 ... Please i need help
Final answer:
The question involves using the Pythagorean theorem to find the missing side 'X' in a right triangle with sides 'X', 4, and 7. 'X' is calculated by rearranging the theorem to X² = c² - b² and plugging in the known values. The equation simplifies to X = √33.
Explanation:
The student is asking for an equation to solve for the missing side of a right triangle, where the sides are given as 'X', 4, and 7. The Pythagorean theorem, which states that a² + b² = c², is the appropriate tool for solving this problem. Since the triangle is right-angled, we assume 'X' is one leg, 4 is the other leg, and 7 is the hypotenuse as it is the longest side.
To find 'X', we rearrange the theorem to solve for the unknown leg (X) as follows: X² = c² - b². Plugging the values into the equation gives us X² = 7² - 4² which simplifies to X² = 49 - 16, hence X² = 33. Consequently, X can be found by taking the square root of 33, which we rewrite as X = √33.