The situation in which the binomial distribution can be approximated to the normal distribution is given by:
(b) a nurse instructs an adult patient to take his resting pulse 10 times over the next few days. a resting pulse requires resting for at least 10 minutes before taking the pulse. the random variable ???? is the number of measurements that are less than 100 beats per minute.
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.The binomial distribution can be approximated to the normal distribution if there are at least 10 failures and 10 successes on the experiment, that is:
np ≥ 10, n(1 - p) ≥ 10.
Meaning that a large number of trials is usually required for the approximation.
In the context of this problem, to achieve the large number of trials needed for the approximation, multiple days are needed to take the observations, hence option b is correct.
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write a new function that is a horizontal stretch of f(x)=(x+2)^3+5
New function that is a horizontal stretch of F(x)=[tex](x+2)^{3} + 5[/tex] is F([tex]\frac{x}{k}[/tex])=[tex](\frac{x}{k} +2)^{3} + 5[/tex]
What is horizontal stretch ?The point (x, y) on the graph of f(x) is changed to the point (x/k, y) on the graph of g when the graph is stretched or contracted horizontally by a factor of 1/k (x).Only when the input value is also increased by a, can a graph be stretched horizontally by a factor of 1/a. The x-coordinates should be multiplied by a once f(x) has been stretched horizontally to f(ax). Keep the y-intercepts where they are. The resulting function might have a different domain, but it will have the same range. If a point (m, n) is stretched horizontally, it becomes (am, n).
F(x)=[tex](x+2)^{3} + 5[/tex]
F([tex]\frac{x}{k}[/tex])=[tex](\frac{x}{k} +2)^{3} + 5[/tex]ch visit :
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A cyclist's speed is 1.5 times faster than a walker's. starting at the same point, after 1.5 hours, they were 12.5 miles apart. what were both of their speeds?
The speed of the cyclist and the walker is 25 miles per hour and 16.67 miles per hour, respectively.
Speed describes how fast an object moves. It can be measured as distance over time.
speed = distance / time
Let x be the speed of the walker and 1.5x is the speed of the cyclist.
If they start "moving simultaneously in the same direction" from the same point and, after 1.5 hours, the distance between them is 12.5 miles, then
distance traveled by cyclist = distance traveled by the walker + 12.5 miles
cyclist's speed(time) = walker's speed(time) + 12.5
1.5x(1.5 hours) = x(1.5 hours) + 12.5
2.25x - 1.5x = 12.5
x = 50/3
walker's speed = 50/3 or 16.67miles per hour
cyclist's speed = 1.5(50/3)
cyclist's speed = 25 miles per hour
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i need help with this, thanks
Answer:
151, 29, 151
Step-by-step explanation:
[tex]m\angle 2=29^{\circ}[/tex] (vertical angles)
[tex]m\angle 1=m\angle 3=151^{\circ}[/tex] (linear pair)
Answer:
[tex]m \angle 1= \boxed{151}\;^{\circ}\\\\m \angle 2= \boxed{29}\;^{\circ}\\\\m \angle 3= \boxed{151}\;^{\circ}[/tex]
Step-by-step explanation:
Angles on a straight line sum to 180°.
⇒ m∠3 + m∠4 = 180°
⇒ m∠3 + 29° = 180°
⇒ m∠3 = 151°
Vertical Angle Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Applying the Vertical Angle Theorem:
m∠2 = m∠4 = 29°m∠1 = m∠3 = 151°john measured two pieces of strings. one piece measured 7/12 m and the other measured 4/7 m. sect the true statement about the lenghts of john strings.
John measured two pieces of string. One piece measured \dfrac7{12}\text{ m}127 mstart fraction, 7, divided by, 12, end fraction, start text, space, m, end text and the other measured \dfrac47\text{ m}74 mstart fraction, 4, divided by, 7, end fraction, start text, space, m, end text.
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
[tex]\sqrt{2x-7} =1[/tex]
Use the image above to identify and explain the relationship between the segments and circles A and B. In your explanation, be sure to include specific vocabulary and definitions for the relationships.
CD
From the given figure, it can be seen that there are two circles with centers A and B respectively.
The circle with the center A is larger in size than the circle with center B. Points P, Q and E lie on the surface of the circle having center A and R, S, C and T points lie on the circle having center B.
Circle A and Circle B's connection
Circle A's size is more significant than Circle B's size.
As a result, circle A's radius exceeds circle B's radius.
The connection between segments
1.
Let M be the location where Segment QT and ER intersect.
Additionally, tangents from an outside point to a circle have identical lengths.
QM = ME———— (1)
MT=MR————(2)
Including (1) and (2)
MR + ME = QM + MT
Q T=ER
2.
Tangents from an exterior point to a circle have identical lengths.
We may write the following segments are equal using this property.
UP=U Q
Z C=ZR
V C=VS
NR=NS
KC=K T
What are Tangents?
A line that only touches a circle or an ellipse at one point is said to be divergent in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve. The following methods can be used to find the tangent equation in differential geometry:
As we are aware, the gradient of the curve at any given location on the curve is equal to the gradient of the tangent to the curve. The following is how to determine the tangent equation of the curve y = f(x):
Utilizing the differentiation principles, determine the gradient function's derivative.
To determine the tangent's gradient, the derivative should be changed to include the provided point's x-coordinate
Find the tangent equation by substituting the provided coordinate point and the gradient of the tangent into the straight-line equation (in a slope-point formula).
Circle's Tangent
A closed, two-dimensional form, a circle is also a curve. The radius of the circle or the line from the center O to the point of tangency is always vertical or perpendicular to the tangent line AB at P, i.e., OP is perpendicular to AB as illustrated in the accompanying picture.
Geometric Tangent
Here, "AB" stands for the tangent, "P" for the point of tangency, and "O" for the circle's center. The OP is the radius of the circle.
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Determine the solution for 0.3(6y + 15) = 1.8y + 4.5. A y=2.5 B y=4.9 C infinite solutions D no Solutions
Answer:
C) infinite solutions
Step-by-step explanation: hope this helps have an amazing rest of ur day <3 ^ ^ :>
Any value of y makes the equation true. All real numbers Interval Notation: (−∞,∞)
The equation given has no solution because they will cancel out each other.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation is;
0.3(6y + 15) = 1.8y + 4.5.
Solving for the variable y;
0.3(6y + 15) = 1.8y + 4.5
Open the bracket;
1.8y + 4.5 = 1.8y + 4.5
Here we can conclude that the equation given has no solution because they will cancel out each other.
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1 find the slope of the slope of the line
2 write an wquation for the like
3 what is the value of a
4 what is the value of b
Answer:
1. Slope= 2
2. [tex] \frac{b - 2}{4 - 2} = 2[/tex] or [tex] \frac{8 - 2}{a - 2} = 2[/tex]
3. a= 5
4. b= 6
Step-by-step explanation:
The slope of a straight line between any two points of the line would be the same. This means that calculating the slope of the line using point (2, 2) and (6, 10) would give us the same slope value when calculating with points (4, b) and (6, 10) for example.
Formula
[tex]\boxed{\text{slope} = \frac{y_1 - y_2}{x_1 - x_2} }[/tex]
Q1. Since we two pairs of known coordinates, let's make use of them in the slope calculation.
Slope of line
[tex] = \frac{10 - 2}{6 - 2} [/tex]
[tex] = \frac{8}{4} [/tex]
= 2
Q2-4. Since in the subsequent parts we will eventually have to find the value of a and b, let's form an equation for each of them.
Slope between (2, 2) and (4, b)= slope between (2, 2) and (6, 10)
[tex] \frac{b - 2}{4 - 2} = 2[/tex]
[tex] \frac{b - 2}{2} = 2[/tex]
Multiply both sides by 2:
b -2= 2(2)
b -2= 4
b= 4 +2
b= 6
Using (2, 2) and (a, 8):
[tex] \frac{8 - 2}{a - 2} = 2[/tex]
Multiply both sides by (a -2):
6= 2(a -2)
Expand:
6= 2a -4
Add 4 to both sides:
2a= 10
Divide both sides by 2:
a= 10 ÷2
a= 5
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Write the domain as an inequality and range as inequality
The domain of the graph as an inequality is
0 ≤ x ≤ ∞The range of the graph as an inequality is
5 < y ≤ ∞How to find the domain and the range of the graphThe domain of a graph is a term that refers to the input values of the graph. The input values are usually in the x axis and this is why we use x in defining the domain
The extreme of the curve on the left side shows the vertex on the x axis is 0 and the curve ended with an arrow showing it is tending to infinity
The range represents the values in the y axis. The curve started at the point y = -5 with a hollow dot. In inequality, a hollow dot means the number is not included hence we use less than.
The graph continued with an arrow this means it tends to infinity
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the schools newspaper staff is selling cookies to raise money for the next school year. the first student who sells 252 boxes earns a laptop. eva sells on average 7 boxes per hour, while Sylvia sells on average 3 boxes every 30 minutes. How much time, in hours, will pass until at least one of the students sells enough boxes to earn a laptop?
A.) 10
B.) 15
C.) 23
D.) 36
E.) 42
A fair cost $33 for admission plus $8 for each roller coaster ride.
Given that n represents the number of roller coaster rides, choose the algebraic expression that models this situation.
A
B
D
41n
33n +8
41
33 + 8n
Super Confused I don’t know what to do right now
Answer:
p=+/- 5/3 or
p =+/- 1 2/3 or
p = +/- 1.66666667
Step-by-step explanation:
Equation
What you have is a quadratic. I am taking the 9 to be a 9 and not a q. So the equation, as I read it, is
9p^2 - 9 = 16 Add 9 to both sides of the equation
Solution
-9+9 + 9p^2 = 16 +9 Combine
9p^2 = 25 Divide by 9
9 p^2 /9 = 25/9 Combine
√p^2 = √(25/9) Take the Square Root of both sides.
p = +/- 5/3
A group of friends decided to buy bulk chocolate from a candy store. If some friends
each want 1/7 of a kilogram of chocolate of the 10 kilograms of chocolate
purchased, then how many people can get a share of chocolate?
Answer:
Your answer is [tex]70[/tex].
Step-by-step explanation:
[tex]10[/tex] ÷ [tex]\frac{1}{7}[/tex] [tex]= 70[/tex]
1.9 Which of the following expressions is equal to -12? Select ALL that apply.
A.-15-3
B.-13-(-1)
C.-8-4
D.-3-(-9)
E.5-17
F. 6-(-6)
213313
The expressions that are equal to -12 are present in Options(B,C, and E).
Solutions of the given expressions are:
A. -15-3
To Add two negative numbers together, start by adding the absolute value of each number together and precede it with a negative sign.
-15-3 = -18
B. -13-(-1)
Proceed by opening the parentheses and modifying the sign in front of it.
-13-(-1) = -13 + 1 = -12
C. -8-4 = -12
D. -3-(-9) = -3 + 9 = 6
E. 5-17
Use the sign of the larger number and subtract to determine the sum of a negative and a positive number.
5-17 = -12
F. 6-(-6) = 6 + 6 =12
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janice was given a piggy bank on her seventh birthday, and she put it to use immediately. each time she puts one or more coins into the piggy bank, she keeps track of the number of coins she has collected to date and the accumulated value of her collection. janice collects only nickels, dimes, and quarters. six months after her seventh birthday, janice looked at her record and ascertained that she had collected 540 coins, which were worth $60. janice counted 100 quarters in her savings. how many nickels and dimes are in her collection?
The number of dimes and nickels in her collection are 296 and 108 respectively.
How to find the number of nickels and dimes?She had collected 540 coins. which were worth $60.
She counted 100 quarters in her saving.
The number of dimes and nickel in her collection can be solved as follows:
Therefore,
let
x = number of dimes
y = number of nickels
number of quarters = 100
Therefore,
x + y + 100 = 504
x + y = 504 - 100
x + y = 404
Hence,
0.1x + 0.05y + 100(0.25) = 60
0.1x + 0.05y = 60 - 25
0.1x + 0.05y = 35
combine the equation
x + y = 404
0.1x + 0.05y = 35
Multiply equation(i) by 0.1
0.1x + 0.1y = 40.4
0.1x + 0.05y = 35
subtract equation(ii) from equation(i)
0.05y = 5.4
divide both sides by 0.05
y = 5.4 / 0.05
y = 108
x = 404 - 108
x = 296
Therefore,
Number of dimes = 296
Number of nickels = 108
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The truth table represents statements p, q, and r. p q r A T T T B T T F C T F T D T F F E F T T F F T F G F F T H F F F Which statements are true for rows A and E? Select two options. p ↔ q q ↔ p q ↔ r r ↔ p r ↔ q
For the truth, table represented the statements that are true for rows A and E are
p ↔ qq ↔ rThis is further explained below.
What is a truth table?Generally, A truth table is a mathematical table that is used in logic, more specifically in linkage with Boolean algebra, boolean functions, and propositional calculus.
It is used to set out the design strength of logical gestures on each of their functional arguments, such that, for each combination of numbers taken by their logical variables.
A truth table is also known as a truth matrix.
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CQ in the correct order is given below
What is the value of x − 9 if x = −24?
Answer:
If x= -24
then the equation will be = -24-9
= -24+ -9
= -33
Therefore the value of x-9 when x=-24 is 33
A car travels at 1/2t^2+55 mph for 0≤x≤5 hours. Approximately how far does it travel?
Select the correct answer.
The sine of the angle based on the information about the cosine is D. ✓91 / 10.
How to illustrate the information?It should be noted that cos is calculated as:
= adjacent / hypothenuse.
This was given as 3/10.
It should be noted that sine = Opposite / Hypothenuse
The opposite will be:
Opp² + Adj² = Hyp²
Opp² + 3² = 10²
Opp² + 9 = 100
Opp² = 100 - 9
Opp² = 91
Opp = ✓91
Therefore, the sine of the angle will be ✓91 / 10
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Twenty-four equals the sum of 10.5 and the quotient of a number and 4.5.
Twenty-four equals the sum of 10.5 and the quotient of a number and 4.5 is given by 24 = 10.5 + x/4.5
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
What is quotient?Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number. As a general rule, the smaller the divisor (denominator) of an expression, the larger would be the quotient.
In order to translate this word problem, we would assign a variable to the unknown number and then translate the word problem into algebraic equation as follows:
Let n represent the unknown number.
Translating the word problem into an algebraic equation, we have;
24 = 10.5 + x/4.5
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What is 183 divided by 13
Answer:
14.077 appr. 14.1
Step-by-step explanation:
183/13=
18÷13=1 remainder 5
53÷13=4 remainder 1
therefore the answer is 14.1
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If sin 25=cos T, what is the value of T?
The value of angle T is 65°
In this question, we have been given sin 25=cos T
We need to find the value of T.
Assuming angle in degrees the value of trigonometric function would be,
sin 25 = 0.4226
As we have been given sin 25=cos T,
cos T = 0.4226
So angle T would be,
⇒ T = arccos( 0.4226)
⇒ T = cos^(-1)( 0.4226)
⇒ T = 65°
Therefore, the value of angle T is 65°
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Gil is shopping for books and CDs. He buys 4 books and no CDs for a total of $32. Write an equation that represents the relationship between the cost of a book, y, and the cost of a CD, x, in standard form.
Gil is out purchasing CDs and books. He spends $32 on 4 books but not any CDs. A standard form equation y=-8n and x=0.
Given that,
Gil is out purchasing CDs and books. He spends $32 on 4 books but not any CDs.
We have to create a standard form equation to show the connection between the price of a book (y) and the price of a CD (x).
The equations in standard form for Gil's change in money after purchasing a book (y) and his change in money after selling a CD (x).
Gil spends $32 on 4 books.
4 books = $32
1 book = $8
If n is the total number of books bought, the change in currency equals
y=-8n.
Here, the negative sign stands for a decline in currency. Here, a slope of -8 indicates that after purchasing each book, the money declined by $8.
There are no CDs so x=0.
Therefore, y=-8n and x=0.
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Could someone help me with this?
When the person picks 170 beads, the number of red beads will be 57.
How to calculate the value?It should be noted that based on the information, the following can be deduced:
Number of red beads = 139
Number of yellow beads = 167
Number of green beads = 107
Total number of beads = 139 + 167 + 107 = 413
Therefore, when one selects 170 beads, the number of red beads will be:
= Number of red beads / Total number × 170
= 139 / 413 × 170
= 57
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Which value is a zero of the function f(x) = x³ − 5x² − 8x + 12?
1 )-1
2)2
3)6
4) 12
Answer:
Only 6 match your answer choices.
Step-by-step explanation:
Solve for x:
x^3 - 5 x^2 - 8 x + 12 = 0
The left-hand side factors into a product with three terms:
(x - 6) (x - 1) (x + 2) = 0
Split into three equations:
x - 6 = 0 or x - 1 = 0 or x + 2 = 0
Add 6 to both sides:
x = 6 or x - 1 = 0 or x + 2 = 0
Add 1 to both sides:
x = 6 or x = 1 or x + 2 = 0
Subtract 2 from both sides:
Answer: x = 6 or x = 1 or x = -2
Does this graph represent a function? Why are why not?
No, because it fails vertical line test.
What is vertical line test?
Vertical line test is defined as a method used to find if the given equation or graph represents a function or not. The vertical line test states that a vertical line needs to cuts the graph of a function (equation) at only one point, for it to represent a function.
Hence, in the given graph, the function intercepts the y- axis at two points, therefore, it fails vertical line test.
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a cell phone user wants to determine what data plan she should get on her new contract. she selects a random sample of 15 months and finds her average usage to be 11.25 gb with a standard deviation of 2.5 gb. she wants to test h0: µ ≥ 12 gb versus ha: µ < 12 gb. what is the p-value for this test? (round your answer to 3 decimal places.)
The p value of the test when the cell phone user wants to determine what data plan she should get is 0.1324.
What is a P value?The p-value is a figure that, when generated from a statistical test, indicates how likely it is that, if the null hypothesis were true, you would have discovered a certain collection of observations. In order to determine whether to reject the null hypothesis, P-values are utilized in hypothesis testing.
The following can be deduced from the information:
Number = 15
Mean = 11.25
Standard deviation = 2.5
Test statistics = -1.162
This is the left tailed test.
The p value will be:
P(z < -1.162 )
This will be looked at in the distribution table
= 0.1324
P-value = 0.1324
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1. $20 haircut; 10% tip
A solid oblique pyramid has a regular pentagonal base. the base has an edge length of 2.16 ft and an area of 8 ft2. angle acb measures 30°. a solid oblique pyramid has a regular pentagonal base. the base has an edge length of 2.16 feet and an area of 8 feet squared. point a is the apex and point c is the center of the hexagon. line a b shows the vertical height of the pyramid. triangle a b c is a right triangle with base length of 7 startroot 3 endroot feet. what is the volume of the pyramid, to the nearest cubic foot? 5 ft3 9 ft3 14 ft3 19 ft3
The volume of the Oblique pyramid is 19 [tex]ft^{2}[/tex]
We know, the volume of a pyramid is [tex]\frac{1}{2}[/tex] × B × h
where B is the area of the base and h is the height of the pyramid.
Given: The pentagonal base has an edge length of 2.16 ft and an area of 8 [tex]ft^{2}[/tex] and angle ACB measures 30°.
Consider triangle ACB
tan30° = [tex]\frac{AB}{CB}[/tex]
[tex]\frac{1}{\sqrt{3} }[/tex] = [tex]\frac{AB}{7\sqrt{3} }[/tex]
AB = 0.58 × [tex]7\sqrt{3}[/tex]
AB = 0.58 × 12.12
AB = 7.03
Now, the volume of the oblique pyramid will be
V = [tex]\frac{1}{2}[/tex] × 8 × 7.03
V = 18.75
V ≈ 19 [tex]ft^{2}[/tex]
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Answer:19
Step-by-step explanation:
x = ____ ( look at photo)