Using the normal distribution and the binomial distribution, it is found that:
a) 43.25% of 10 year old's cannot go on this ride.
b) There is a 0.7814 = 78.14% probability that at least two of them will be able to ride Batman the Ride.
c) There is a 0.1062 = 10.62% probability that the first 10 year old you see who can ride Batman the Ride is the 3rd 10 year old who enters the park.
d) There is a 0.0834 = 8.34% probability that the 5th 10 year old you see who can ride Batman the Ride is the 12th 10 year old who enters the park.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.In the context of this problem, the mean and the standard deviation are given as follows:
[tex]\mu = 55, \sigma = 6[/tex]
For item a, the proportion is the p-value of Z when X = 54, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (54 - 55)/6
Z = -0.17.
Z = -0.17 has a p-value of 0.4325.
Hence the percentage is of 43.25%.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.For item b, the parameters of the binomial distribution are given as follows:
p = 0.5675, n = 4.
Hence:
P(X = 2) = 6 x (0.5675)² x (0.4325)² = 0.3615.P(X = 3) = 4 x (0.5675)³ x (0.4325)¹ = 0.3162.P(X = 4) = (0.5675)^4 = 0.1037.Hence:
P(X >= 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.3615 + 0.3162 + 0.1037 = 0.7814.
Which is the probability.
For item c, the probability is given as follows:
p x P(X = 0 with n = 2).
Hence:
p = 0.5675 x (0.4325)² = 0.1062.
For item d, the probability is given as follows:
p x P(X = 4 with n = 11). (inverse binomial).
Hence:
0.5675 x (11!)/(5! x 6!) x (0.5675)^4 x (0.4375)^7 = 0.0834.
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Which is the best description of the graph of the derivative of a parabola that opens downward?
let's take a looksie hmmmm a parabola opening downwards in vertex form using constants of "h" and "k" will be like
[tex]y = -(x+h)^2 +k\implies y = -x^2-2hx-h^2+k \\\\\\ \cfrac{dy}{dx}=-2x-2h\qquad \impliedby \textit{straight line with a negative slope}[/tex]
Write the following comparison as a ratio reduced to lowest terms.
114 hours to 13 days
The ratio of 114 hours to 13 days is 19:52.
How to calculate the ratio?It should be noted that ratio is simply used to show the comparison between two things that are illustrated.
In this case, we want to calculate the ratio of 114 hours to 13 days. It should be noted that 24 hours make one day. Therefore, 13 days will be:
= 13 × 24 = 312 hours.
The ratio of 114 hours to 13 days will be:
= 114 / 312
= 19 / 52
The ratio is 19:52.
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Salma has a points card for a movie theater.
• She receives 30 rewards points just for signing up.
• She earns 8.5 points for each visit to the movie theater.
• She needs 115 points for a free movie ticket.
Which equation or tape diagram could be used to represent the
context if a represents the number of visits Salma must make to earn
a free movie ticket?
using linear equation, Salma needs 10 number of visit to movie theater to get free movie ticket.
What is Linear equation?
A linear equation is one in which the variable's highest power is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation. A linear equation with two variables has the formula Ax + By = C as its standard form. Here, the variables are x and y, the coefficients are A and B, and the constant is C.
linear equation is given by y= mx + c
Salma has 30 rewards points just for signing up and 8.5 points for each visit. the equation became 30+8.5v=115
30+8.5v=115
8.5v=115-30
8.5v=85
v=10
therefore, she needs 10 number of visits to movie theater.
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Identify The Function Family Sketched Below
The function family sketched is exponential function.
From the graph, we can find certain values of the function for certain x-values.
When x = 0, the function has value 1.
When x = 2, the function has value 4
When x = 3, the function has value 8.
When x = 4, the function has value 16
From this we can identify the function as the exponential function, f(x) = eˣ
because e⁰ = 1. i.e., exponential function has value 1 when x = 0 which satisfy the sketch of the function given.
Also the other options given as piecewise function, linear function and quadratic function.
A piecewise function will not have a continuous sketch, but here the sketch of the function is continuous. So it cannot be a piecewise function. A linear function will have the sketch as a straight line, but here it is not. So it is not a linear function. The function values given in the sketch does not satisfy the quadratic function also.
So the only option is the sketch is of the exponential function.
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The graph of an absolute value function f(x) = a|x| includes the point (1, 8). Complete the following statements.Another point on the graph is ( ?, 8).The value of a is
In a absolute value graph the value of y is the same in -x and x.
Then if the coordinates (x,y) one point is (1, 8), the graph have another point in (- 1, 8).To find the value of a you use one of the points (x,y) in the general form of absolute value:
( 1 , 8) x=1 f(x)= y=8
[tex]8=a\lvert1\rvert[/tex]As:
[tex]\lvert\pm a\rvert=a[/tex]You get:
[tex]8=a\cdot1[/tex]Then:
[tex]a=8[/tex]The equation for the graph with points (1 , 8) and ( -1, 8) is:
[tex]f(x)=8\lvert x\rvert[/tex]a= 8Find the perimeter of the following figure with the indicated dimensions.
Givens.
• The diameter of the semi-circle is 9.25 yd.
,• The other two sides of the triangle are 6.83 yd and 8.66 yd long.
First, find the perimeter of the semi-circle using the circumference formula.
[tex]\begin{gathered} C_{\text{semi}}=\frac{\pi\cdot d}{2}=\frac{\pi\cdot9.25yd}{2} \\ C_{\text{semi}}\approx14.52yd \end{gathered}[/tex]Second, add the two sides of the triangle to the circumference of the semi-circle.
[tex]\begin{gathered} P=14.52yd+6.83yd+8.66yd \\ P=30yd \end{gathered}[/tex]Therefore, the perimeter of the figure is 30 yards.The perimeter of the rectangle below is 104 units. Find the length of side AD.
Write your answer without variables.
D
52-2
4z
C
B
AD =
0
HELP PLEASE!
Answer: 28
Step-by-step explanation:
Using the formula for the perimeter of a rectangle,
[tex]2(5z-2+4z)=104\\\\9z-2=52\\\\9z=54\\\\z=6\\\\\therefore AD=5(6)-2-28[/tex]
Hello! May I please have some help with this?
Answer:
12
Step-by-step explanation:
The calculation for x=0x=0 corresponds to the
point where the graph crosses the______-axis.
This is the point (______)
The calculation for x=0 corresponds to the point where the graph crosses the y-axis . This is the point (0,y) .
In the question ,
it is given that x=0 ,
When x=0 in a point (x,y) means , that point lies on the y -axis , and it is called as the y intercept .
Y intercept is defined as the point where the graph of a line crosses the y-axis .
the point on the y-axis will be (0,y) ,
So , the graph will cross the y-axis when x=0 , and that point will be (0,y).
and the value of y will be called as the y intercept of the graph .
Therefore , the calculation for y=0 corresponds to the point where the graph crosses the y-axis . This is the point (0,y) .
The given question is incomplete , the complete question is
The calculation for x=0 corresponds to the point where the graph crosses the________-axis. This is the point (______) .
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simplify the expression (-6)^-4 using positive exponents
there u gooooooooooooooooooooooooooooooooo
need help with this one
Applying the relations given, considering equivalent angles, the trigonometric measures for the angles are given as follows:
sin(240º) = -sqrt(3)/2.cos(225º) = -sqrt(2)/2.tan(225º) = 1.How to find the sine of 240º?The sine of 240º can be written as follows:
sin(240º) = sin(180º + 60º).
Applying the first relation given on the second line, we have that:
sin(180º + 60º) = -sin(60º)
It is known that sin(60º) = sqrt(3)/2, hence the sine of 240º is given as follows:
sin(240º) = -sin(60º) = -sqrt(3)/2.
How to find the cosine of 225º?The cosine of 225º can be written as follows:
cos(225º) = cos(180º + 45º).
Applying the second relation given on the second line, we have that:
cos(180º + 45º) = -cos(45º)
It is known that cos(45º) = sqrt(2)/2, hence:
cos(225º) = -cos(45º) = -sqrt(2)/2.
How to find the tangent of 225º?The tangent of 225º can be written as follows:
tan(225º) = tan (180º + 45º).
Applying the third relation given on the second line, we have that:
tan(180º + 45º) = tan(45º)
It is known that tan(45º) = 1, hence:
tan(225º) = tan(45º) = 1.
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Let f(x)=−3x−1 and g(x)=x2− 1. Find (f◦g)(−1).
The value of composite function (f о g) (-1) will be -1.
What is Composite function?
A composite function is a function that is written inside with another function and composition of functions is done by substituting one function into another function.
Given that;
The value of functions are;
f (x) = - 3x -1
And, g (x) = x² - 1
Now, All values of functions are;
f (x) = - 3x -1
And, g (x) = x² - 1
Composition of functions is calculated as;
Since, (f о g) (x) = f (g(x))
Substitute the value of function f(x) and g(x) in above equation;
(f о g) (x) = f (g(x))
= f (x² - 1)
= - 3(x² - 1) - 1
= -3x² + 3 - 1
= -3x² + 2
Put x = -1 in above equation we get;
(f о g) (-1) = - 3 (-1)² + 2
= - 3 + 2
= -1
So, (f о g) (-1) = -1
Thus, The value of composite function (f о g) (-1) will be -1.
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PLEASE HELP ASAP 50 POINTS, I will mark brainlyest i would appreciate if shown how to do it with steps
If m∠SPR = 61 and m∠SPQ = 121, what is m∠QPR?
Answer:
121 - 61 = 60 degrees
Step-by-step explanation:
Answer:
∠QPR=60
Step-by-step explanation:
∠SPQ-∠SPR=∠QPR
121-61=∠QPR
60=∠QPR
A DVD is discounted by 15% and then from the already discounted price, a further 20% discount is given. If the price now is $300, find the original price?
The original price is $414.
What is discount?The difference between the purchase price and the item's par value is the discount. Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided. a fair deduction from a debt account, typically done in exchange for cash or quick payment.
Given Data
A DVD is discounted by 15% and then from the already discounted price, a further 20% discount is given.
The price now is $300
x = 300 + 15% + 20%
x = 300 + [tex]\frac{15}{100}[/tex] + [tex]\frac{20}{100}[/tex]
x = 414
The original price is $414.
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Question 3 (1 point)Find the value of x so that the function has the given value.j(x) = 4x + 11; 13CBlank 1:
A function is a relation in which each input value (x-value) has one and only one output value (y-value).
You have the following Linear function:
[tex]j\mleft(x\mright)=4x+11[/tex]According to the explained in the problem, you must find an input value that gives you 13 as the output value. Knowing this, you can say that:
[tex]j(x)=13[/tex]Substitute this value into the given function:
[tex]\begin{gathered} j(x)=4x+11 \\ 13=4x+11 \end{gathered}[/tex]The final step is to solve for "x".
Therefore, the value of "x" so that the function has the given value 13, is:
[tex]\begin{gathered} 13-11=4x \\ 2=4x \\ \frac{2}{4}=x \\ \\ x=\frac{1}{2} \end{gathered}[/tex]W QUESTIONS 100 POINTS WILL GIVE BRAINLYEST
The areas for this problem are given as follows:
3. 681.25 ft².
4. 193 m².
Item 3The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:
A = lw.
For this problem, a rectangular deck of dimensions l = 18.75 ft and w = 15 ft is added, hence the area of the deck is:
A = 18.75 x 15 = 281.25 ft².
This area is added to the previous area, hence the total area is of:
A = 400 ft² + 281.25 ft² = 681.25 ft².
Item 4The figure is composed by:
A rectangle of dimensions 10 m and 18 m.A triangle of base 13 m and height 2 m.The area of the triangle is half the base times the height, while the area of the rectangle was presented in the previous item, hence the total area of the figure is:
A = 10 x 18 + 0.5 x 13 x 2 = 180 + 13 = 193 m².
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Three sides of a quadrilateral are the same length, q. The length of the fourth side is 7 inches. The perimeter of the quadrilateral is 40 inches. Write an equation that represents the situation.
The equation that represent the situation of the quadrilateral is 40 = 3q + 7
How to write equation to represent the side of a quadrilateral?A quadrilateral is a polygon with 4 sides.
Three sides of a quadrilateral are the same length, q.
The length of the fourth side is 7 inches.
The perimeter of the quadrilateral is 40 inches.
The equation to represent the situation is as follows:
perimeter of a figure is the sum of the whole sides.
Hence,
perimeter of the quadrilateral = q + q + q + 7
perimeter of the quadrilateral = 3q + 7
Therefore,
40 = 3q + 7
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Answer:
3q + 7 = 40
Step-by-step explanation:
I got this lesson
(a) For each pool, write an expression for the amount of water in the
gool after x minutes
Two pools are being filled with water. To start, the first pool had 817 liters of water and the second pool was empty. Water is being added to the first pool at a
rate of 19 liters per minute water is being added to the second pool at a rate of 38 liters per minute.
Leta be the number of minutes water has been added.
Amount of water in the first pool (In liters) =
Amount of water in the second pool (in liters) =
(b) Write an equation to show when the two pools would have the
same amount of water
(a) Amount of water in the first pool (In liters) = (817 + 19x) liters
Amount of water in the second pool (in liters) = 39x liters
(b) An equation to show when the two pools would have the same amount of water is 817 + 19x = 38x.
Given:
For the First Pool :
Initial amount of water in the Pool = 817 liters
Water is being added to the first pool at a rate of 19 liters per minute.
Amount of water added after x minutes = 19x
So, Total amount of water after x minutes = (817 + 19x) liters
For the Second Pool:
It was empty initially.
Water is being added to the second pool at a rate of 38 liters per minute.
Amount of water added after x minutes = 38x
So, Total amount of water after x minutes = 38x liters
Now to determine an equation to show when the two pools would have the same amount of water.
817 + 19x = 38x
38x - 19x = 817
19x = 817
x = 817/19
x = 43 minutes
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Select the postulate that specifies the minimum number of points in space.
Postulate 1: A line contains at least two points.
Postulate 1a: A plane contains at least three points not all on one line.
Postulate 1b: Space contains at least four points not all on one plane.
Postulate 2: Through any two different points, exactly one line exists.
•
Postulate 3: Through any three points that are not one line, exactly one plane exists.
Postulate 4: If two points a lie in a plane, the line containing them lies in that plane.
Postulate 5: If two planes intersect, then their intersection is a line.
The postulate specifies the minimum number of points in space is, Postulate 1b: Space contains at least four points not all on one plane.
A postulate is an assumption or a claim that is made without providing any supporting evidence. The fundamental claims that are used to support other claims known as theorems are known as postulates. Once a theorem is established, it can be applied to the establishment of other theorems.
By examining each postulate, we may effectively respond to this query.
Postulate 1a: establishes that if G and H are distinct points on plane R, then R contains a third point rather than GH.
Postulate (1b): establishes the bare minimum within a space.
Postulate 1: This describes a line segment with two points, say A and B.
Postulate 2: It asserts that two points determine a line.
Postulate 3: This one explains why, for example, if one leg is shorter than the other three, a table with four legs would wobble, but a table with three legs would not wobble.
Postulate 4: When points A and B are in Q, it is confirmed that AB is in plane Q.
Postulate 5: It concerns two planes.
According to the data presented above, the appropriate response to our query is:
Postulate 1b: Space contains at least four points not all on one plane.
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What is the translation of y=x^2 shifted left 3 units
Original equation: y = x²
Tranformation rule:
horizontal translation c units leftt = f(x + c); so:
Modified equation: y = (x + 3)²
Find the indicated z score. The graph depicts the standard normal distribution with
mean 0 and standard deviation 1.
The indicated z score is
(Round to two decimal places as needed.)
Z 0
0.8289
Using the normal distribution, it is found that the indicated z-score is Z = 1.08. A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution.
What is meant by standard normal distribution?A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard normal distribution is centered at zero, and the standard deviation indicates how much a specific measurement deviates from the mean.
While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
The z-score of a measure X in a normal distribution with mean and standard deviation is given by:
z = (x-μ)/σ,
It counts the number of standard deviations the value deviates from the mean.
We look at the z-score table after determining the z-score to determine the p-value, which is the percentile of X.
We want Z in this problem to have a p-value of 0.8599, thus Z = 1.08.
The complete question is,
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.8599.
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Please help I’ll mark you as brainliest if correct!!
Answer:
4 6 3
_ 1 3 9
________
3 2 4
Step-by-step explanation:
you think of of a number
or use logic to answer it
The sum of three numbers is 80. The first number is 8 more than the second. The third number is 2 times the second. What are the numbers?First number:Х?Second number:0Third number:
Let's use the variables x, y and z to represent each of the three numbers.
If the sum of the three numbers is equal to 80, we have our first equation:
[tex]x+y+z=80[/tex]The first number is 8 more than the second, so:
[tex]x=y+8[/tex]The third number is 2 times the second, so:
[tex]z=2y[/tex]Using these values of z and x in the first equation, let's solve it for y:
[tex]\begin{gathered} (y+8)+y+(2y)=80 \\ 4y+8=80 \\ 4y=72 \\ y=18 \end{gathered}[/tex]Now, calculating x and z, we have:
[tex]\begin{gathered} x=18+8=26 \\ z=2\cdot18=36 \end{gathered}[/tex]Therefore the first number is 26, the second number is 18 and the third number is 36.
Ozzie filled up the gas tank of his truck and headed out on a road trip. The x- axis on the graph below shows the number of miles Ozzie drove since filling up. The y- axis represents the number of gallons of gas in the truck’s gas tank. Find the x- and y- intercepts. Explain what the x- and y- intercepts mean for Ozzie.
Okay, here we have this:
Considering the provided information, we are going to find the x- and y- intercepts and explain its meaning. So we obtain the following:
Since the x-intercept is the point where the Graph intersects the x-axis (y=0) and the y-intercept is the point where the Graph intersects the y-axis (x=0), we have that:
x-intercept=(300, 0)
y-intercept=(0, 16)
Since the y-axis represents the number of gallons, and the x-axis time, then the y-intercept indicates that when filling the tank it was left with 16 gallons, and the x-intercept indicates that when emptying the tank had traveled 300 miles.
1/5 (x-2)= 1/10 (x +6)
Answer: The answer is 10
Step-by-step explanation:
Distribute 1(x-2)/5 = 1(x+6)/10
x-2/5 = x+6/10
Multiply by 10 on each side
2(x - 2) = x + 6
Distribute
2x - 4 = x + 6
Add 4 on each side
2x= x + 10
Subtract x
x = 10
Answer: x=10
Step-by-step explanation:
1/5(x-2)=1/10(x+6)
Distribute and multiply first
(1/5*x) -(1/5*2)=(1/10*x) +(1/10*6)
1/5x-2/5=1/10x+6/10
We do not have the same denominators on both sides. 5 goes into 10 two times so we will multiply everything on the left by 2 to get a common denominator.
2/10x-4/10=1/10x+6/10
Subtract 1/10x from both sides
1/10x-4/10=6/10
Add 4/10 to both sides
1/10x=10/10
1/10x= 1
Multiply both sides by 10/1 (the fraction inverse) to get rid of the fraction.
(10/1)(1/10x) =(1)(10/1)
x= 10
Check work:
1/5(x-2)=1/10(x+6)
Substitute your answer for x
1/5(10-2)=1/10(10+6)
1/5(8)=1/10(16)
8/5=16/10
Simplify 16/10 by dividing by 2
8/5=8/5
If x2=16, find x3?
If x3=125, find x2
Answer:balls
Step-by-step explanation:your mom
−[4.2−3(2.1)](−0.2)2+1
Write the sentence as an equation.
40 is equal to 208 subtracted from the product of 184 and j
Type a slash (/) if you want to use a division sign.
Answer:
40 = (184*j) - 208 or 40 = 184j - 208
can you help me please
The given expression is 4.9 x 10⁻¹¹.
What is a mathematical expression?
An expression, often known as a mathematical expression, is a limited collection of symbols that have been well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and groupings can all be represented by mathematical representations, which can also be used to indicate the logical syntax's sequence of operations and other features. However, in contemporary mathematics, and particularly in computer algebra, formulae are seen as expressions that, depending on the values supplied to the variables present in the expressions, can be evaluated to true or false.
The given expression can be solved as follows
(7x10⁻⁶)(7x10⁻⁶)
= (7x7) x (10⁻⁶x10⁻⁶)
= 49 x 10⁻¹²
= 4.9 x 10⁻¹¹
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if f(x)=-5, what is x?
Answer:
x = -5/f
Step-by-step explanation:
a) Divide both sides by f.
fx/f = -5/f
x = -5/f
Answer:
the answer is -5/f
Step-by-step explanation:
f(x)=fx
fx=-5
Divide both sides by f
fx/f =-5/f
x=-5/f
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