Answer: 0.098
Step-by-step explanation: First you’ll need to find the sample distribution mean and standard deviation (which is 78 and 1.55). Then you plug it into calculator using normal approximation cause n is large: normalcdf(80,100,78,1.55)
As, 0.098 proportion of these samples would, we expect to have a mean greater than 80. Thus, option (C) is correct.
What is the population?As the population is defined, as a group of groupings with a common characteristic. In data point, a population is the pool of individuals from which a statistical sample is drawn for a study. As we see, different countries have different populations.
As here the μ = 78, σ = 1.5492 and x = 80
We need to compute P(X >= 80). The corresponding z-value is calculated using Central Limit Theorem
z = (x - μ)/σ
z = (80 - 78)/1.5492 = 1.29
Therefore,
P(X >= 80) = P(z <= (80 - 78)/1.5492)
= P(z >= 1.29)
= 1 - 0.902 = 0.098
Therefore, The right option (B) is correct
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a bag of apples and oranges contains twice as many apples as oranges. if there are 15 total pieces of fruit in the bag how many apples are in the bag
Considering the definition of an equation and the way to solve it, there are 10 apples in the bag.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.
The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Amount of apples in the bagBeing "or" the number of oranges in the bag, and knowing that:
A bag of apples and oranges contains twice as many apples as oranges.There are 15 total pieces of fruit in the bag.the equation in this case is:
or + apples= 15
or + 2or= 15
Solving:
3or= 15
or= 15 ÷ 3
or= 5
As a bag of apples and oranges contains twice as many apples as oranges, then 2or= 2×5= 10 apples
Finally, there are 10 apples in the bag.
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Ая
Hola
مهم
Warm Up
What is the exact distance between the points (4,-2) and (-6,4)?
Select the correct answer.
O 4√10
O2√34
O2√26
O 10√6
Submit
The distance between two points (4,-2) and (-6,4) exists [tex]2\sqrt{34}.[/tex]
How to estimate the distance between two points?Distance between two points exists the length of the line segment that joins the two given points. Distance between two points in coordinate geometry can be estimated by finding the length of the line segment merging the provided coordinates.
Let the points be (4,-2) and (-6,4).
The distance between two points [tex](x_{1} ,y_{1})[/tex] and [tex](x_{2} , y_{2} )[/tex] exists provided by the distance between the two points
[tex]= $\sqrt\\(x_{2} -x_{1} )^{2} +(y_{2} -y_{1})^{2}[/tex]
substituting the points in the equation, we get
[tex]$=\sqrt\\(-6-(4)^{2} +(4-(-2)^{2}[/tex]
simplifying the equation, we get
[tex]$=\sqrt{136}[/tex]
[tex]$=2\sqrt{34}[/tex]
The distance between two points (4,-2) and (-6,4) exists [tex]2\sqrt{34}.[/tex]
Therefore, the correct answer is option c. [tex]$2\sqrt{34}.[/tex]
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Take some time to fill in your notes, the area that is not shown in this video. Fill in the table with the values you think are the x-values and the y-values, write them as ordered pairs, then write them as a ratio in y/x form. In the table, which are the y-values and which are the x-values [Time(s) or Heartbeat(s)]?
The x-values are the heartbeat(s) and the y-values are the time(s)
How to determine the x and y values?The variables are given as:
Time(s) and Heartbeat(s)
As a general rule, the action that is being done is the independent variable.
The action here is the heartbeat.
So, the x-values are the heartbeat(s) and the y-values are the time(s)
A possible value of this is;
x = 100, y = 60 seconds
So, the ordered pair is (100,60)
When represented as ratio, we have;
Ratio = 60/100
Simplify
Ratio = 0.6 heartbeat per second
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please and a girl out, and if you can explain how you got the answer so i can undertsnad myself
Answer:
9cm
Step-by-step explanation:
If the triangles are similar then their lengths are in a ratio to each other, Ex: PR is 3 times LN, 2*3 = 6cm
This gives us a ratio of 1:3
PQ = LM*3 = 3cm*3 = 9cm
v = u + at
if v=10,t=2,and u=5,find the value of a
Answer:
2.5
Step-by-step explanation:
v = u + at is one of the kinematics equations.
Given v = 10, t = 2, u = 5, we will substitute these values into the equation to find a.
[tex]v = u + at\\10=5+2a\\2a=10-5\\2a = 5\\a = \frac{5}{2} \\= 2.5[/tex]
*Find the formula of the series 1+2²+3²+4²+....+n²*
The formula is [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
What are series?
In mathematics, we can describe a series as adding infinitely many numbers or quantities to a given starting number or amount.
We will find the formula as shown as below:
Let [tex]S=1+2^2+3^2+4^2+................+n^2[/tex]
We know [tex](n+1)^3=n^3+3n^2+3n+1[/tex]
[tex](1+1)^3=1^3+3(1)^2+3(1)+1[/tex]
[tex](2+1)^3=2^3+3(2)^2+3(2)+1[/tex]
[tex](3+1)^3=3^3+3(3)^2+3(3)+1[/tex]
.
.
[tex](n+1)^3=n^3+3(n)^2+3(n)+1[/tex]
On adding
[tex]2^3+3^3+4^3......(n+1)^3=(1^3+2^3+3^3+.....+n^3)+3(1^2+2^2+.....+n^2)+3(1+2+3....n)+(1+1+1+....+1)[/tex]
[tex]2^3+3^3+4^3......(n+1)^3-(1^3+2^3+3^3+.....+n^3)=3S+\frac{3n(n+1)}{2}+(1+1+1+....+1)[/tex]
[tex](n+1)^3-1^3=3S+\frac{3n(n+1)}{2} +n[/tex]
[tex]n^3+3(n)^2+3(n)+1-1=3S+\frac{3n(n+1)}{2} +n[/tex]
[tex]2n^3+6n^2+6n=6S+3n^2+3n+2n[/tex]
[tex]6S=2n^3+3n^2+n[/tex]
[tex]6S=2n^2(n+1)+n(n+1)[/tex]
[tex]6S=(n+1)(2n^2+n)[/tex]
[tex]6S=n(n+1)(2n+1)[/tex]
[tex]S=\frac{n(n+1)(2n+1)}{6}[/tex]
Hence, the formula is [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
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Which expression would be easier to simplify if you used the commutative property to change the order of the numbers?
A. 1/7 + (-1)+ 2/7
B. - 15+(-25) +43
C. 120+80+(-65)
D. 40+10+(-12)
The order of the numbers which satisfies commutative property exists 1/7 + (-1)+ 2/7.
What is meant by commutative property?
The commutative property exists a math rule that states that the order in which we multiply numbers does not change the product. The commutative property uses for addition and multiplication. The property states that phrases can “commute,” or transfer locations, and the outcome will not be affected. This exists described as a + b = b + a for addition, and a × b = b × a for multiplication.
Arranging the order of the numbers the fractions
[tex]$& \frac{1}{7}+(-1)+\frac{2}{7} \\[/tex]
[tex]$=& \frac{1}{7}+\frac{2}{7}+(-1) \\[/tex]
Simplifying the equation, we get
[tex]$= \frac{1}{7}+(-1) \\[/tex]
[tex]$&=\frac{4}{7}[/tex]
Therefore, the correct answer is option A. 1/7 + (-1)+ 2/7
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---------------------
Answer:-----------
Step-by-step explanation:------------------
Answer:
???????
Step-by-step explanation:
Please tell the question so i can answer it
WORTH 10 POINTS PLEASE HELP!!!!!!!!!!!!!!!
Consider the functions graphed below. A curve a intersects a parabola b at (negative 1, 0 point 5) and a parabola c at (negative 2 point 4, 0 point 3). A diagonal curve d intersects the parabola b at (0 point 5, 0) and (2, 3) and parabola c at (negative 1 point 2, negative 1 point 2). Determine which function has the greatest rate of change over the interval [0, 2]. A. d B. b C. c D.
Answer:
Step-by-step explanation:
The function with the greatest rate of change over the interval [0, 2] is: D. a
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Place the indicated product in the proper location on the grid.
(x + 2y ) 2
The expansion of the expression (x + 2y)² is x² + 4xy + 4y².
How to illustrate the information?The given expression is (x + 2y)². The expansion of the expression will be:
(x + 2y)²
= (x + 2y)(x + 2y)
= x² + 2xy + 2xy + 4y².
= x² + 4xy + 4y²
The expansion is x² + 4xy + 4y².
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A new Outdoor Recreation Center is being built in Hadleyville. The perimeter of the rectangular playing field is 318 yards. The length of the field is 5 yards less than
triple the width. What are the dimensions of the playing field?
yards.
Answer:
41 yards by 118 yards
Step-by-step explanation:
Let W and L be the Width and Length of the playing field:
The perimeter, P, would be P = 2W + 2L
We are told that P = 318 yards.
We learn that L = 3W - 5
Combining this information, we can say:
P = 2W + 2L [Oriinal equation]
318 = 2W + 2L [P is 318]
318 = 2W + 2(3W-5) [ Use the definition of L = 3W - 5]
318 = 2W + 6W - 10
328 = 8W
W = 41 yards
Use this value of W to find L:
L = 3W - 5
L = 3(41) - 5
L = 123 - 5
L = 118
CHECK
Does 2*(118) + 2*(41) = 318? YES
Is the length 5 yards less than triple the width?
3*(41) - 5 = 118 YES
What’s 98 divided by 82 + 283 multiplied by 69 - 29
The solution to the given expression [98/(82 + 283)] * (69 - 29) is; 784/73
How to solve simple arithmetic operations?
We want to solve the expression;
[98/(82 + 283)] * (69 - 29)
Let us first simplify the first part which is;
98/(82 + 283) = 98/365
Then let us simplify the second part which is;
69 - 29 = 40
Thus, we have the expression;
(98/365) * 40
This can be simplified further to get;
(98/73) * 8 = 784/73
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John has a few shoes. mike has 10 shoes more than john. james has 8 less than john. mike has two times of james, how many shoes does john have
Step-by-step explanation:
M=2G
M=J+10
G=J-8
2G=J+10
G=J-8
2(J-8)=J+10
2J-16=J+10
J=26
Triangle is reflected across the y-axis and then dilated by a factor of centered at the origin. Which statement correctly describes the resulting image, triangle ?
Image of right triangle ABC in a graph with vertices A (minus 4, minus 2), B (4, minus 2), and C (4, 4)
A.
The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths.
B.
Both the reflection and dilation preserve the side lengths and angles of triangle .
C.
Neither the reflection nor the dilation preserves the side lengths and angles of triangle .
D.
The dilation preserves the side lengths and angles of triangle . The reflection does not preserve side lengths and angles.
Answer:
A. The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths.
Step-by-step explanation:
Reflection is a rigid transformation. It preserves both angles and side lengths. Dilation preserves angles, but changes all lengths by the same scale factor.
ApplicationThe described triangle was subject to reflection, which preserves angles and lengths. It was also subject to dilation, which preserves angles, but not lengths.
The appropriate description is that of choice A.
Which function describes this graph?
[tex]f(x) = (x + 3)(x + 6) \\ f(x) = x {}^{2} + 6x + 3x + 18 \\ f(x) = x {}^{2} + 9x + 18[/tex]
Option CAnswer:
C.) y = x² + 9x + 18
Step-by-step explanation:
C.) is correct because the function has the accurate x-intercepts. X-intercepts are the x-values in which the line passes through the x-axis. We can prove this by setting the function equal to 0, factoring, then solving for "x". You can factor the function by asking yourself the question, "which two numbers multiply to 18 and add to 9?"
y = x² + 9x + 18 <----- Original function
0 = x² + 9x + 18 <----- Set the function equal to 0
0 = (x + 6)(x + 3) <----- Factor
0 = x + 6 0 = x + 3
-6 = x -3 = x
So, at (-3, 0) and (-6, 0), the function crosses the x-axis. This matches the given graph.
Find the exact value of sin 5pi/4
The exact value of sin 5π/4 is 0. 0677
How to find the value
It is important to note that π = 3. 142
Let's find sin 5π
Substitute the value
sin 5π = sin (5 × 3. 142) = sin 15. 71
= [tex]\frac{sin 15. 71}{4}[/tex]
Find the sine of the number
= [tex]\frac{0. 27076}{4}[/tex]
= [tex]0. 0677[/tex]
Thus, the exact value of sin 5π/4 is 0. 0677
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Answer:
- sqrt2/2
Step-by-step explanation:
PLEASE HELP IM STUCK
Answer:
-3
Step-by-step explanation:
look at the hint: slope (most call it gradient) = change in y/change in x
so you take 2 x and y variables and subtract
15 - 9 = 6 ← change in y
0 - 2 = -2 ← change in x
slope (gradient) = 6/-2
slope (gradient) = -3
Ivan began to prove the law of sines using the diagram and equations below.
Triangle A B C is shown. A perpendicular bisector is drawn from point C to point D on side B A to form a right angle. The length of the perpendicular bisector is h, the length of C B is a, the length of C A is b, and the length of B A is c.
sin(A) = h/b, so b sin(A) = h.
sin(B) = h/a, so a sin(B) = h.
Therefore, b sin(A) = a sin(B).
Which equation is equivalent to the equation
b sin(A) = a sin(B)?
StartFraction a Over sine (uppercase B) EndFraction = StartFraction b Over sine (uppercase A) EndFraction
StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction
StartFraction sine (uppercase A) Over sine (uppercase B) EndFraction = StartFraction b Over a EndFraction
StartFraction sine (uppercase B) Over a EndFraction = StartFraction sine (uppercase A) Over b EndFraction
An equation which is equivalent to the equation bsin(A) = asin(B) is: B. [tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
What is the law of sines?The law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.
Mathematically, the law of sines is given by this equation:
[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
In this context, we can infer and logically deduce that an equation which is equivalent to the equation bsin(A) = asin(B) is [tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex].
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Answer: B
Explanation: sin(A)/a=sin(B)/b
URGENT!!!!!!
A researcher orders a broth of 8.8% glucose for her lab. However, she needs a stronger broth, one that is 13.8% glucose. Fortunately, she has 69.7 liters of 39.4% glucose broth in the stock room. How much 13.8% glucose broth can she make? Round your answer to the nearest tenth of a liter.
Answer:426.6
Step-by-step explanation:
.138 x =.088(x - 69.7) + .394(69.7)
.138 x - .088x = 69.7(.394 - .088)
.05x = 21.3282
/
x = 426.564
This rounds to x = 426.6
Give me brainliestThe image point of A after a translation right 4 units and up 2 units is the point B(1,−3). Determine the coordinates of the pre-image point A.
The image of point A(-3, -5) after a translation right 4 units and up 2 units is the point B(1,−3)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
The point A = (1 - 4, -3 - 2) = (-3, -5)
The image of point A(-3, -5) after a translation right 4 units and up 2 units is the point B(1,−3)
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| 9. The distance between Town A and Town B was 108 km. A car and a van left Town A at 12 00 for Town B. On reaching Town B, the car returned to Town A by the same route. When the two vehicles met, the distance that the car and the van had travelled was in the ratio 7:5. The average speed of the van was 60 km/h. Calculate
a) the time at which the two vehicles met, and
b) the average speed of the car in km/h.
Someone please helppp
Answer:
a) Time until both vehicles meet is 1.5 hours after starting at noon. That makes it 1:30PM.
b) Average speed of car is 84 km/h
Step-by-step explanation:
A -----------------------z------------B
Left Speed(km/h) Time
Car: 12PM X
Van: 12PM 60
Car/Van
DistanceCar AB + z
DistanceVan Az
Ratio: (AB+z)/Az = 7/5
Time until both meet = T (in hours)
Distance Car: xT
Distance Van: 60T
====
xT = AB + z
60T = Az
---
(xT/60T)= (7/5)
x = 60(7/5)
x = 84 km/h
=====
Time for car to reach B is: time (hr) = 108 km/(84 km/h)
time = 1.286 hours
Distance for at 1.289 hours is: distance (km) = (60 km/h)*(1.286 h)
distance = 77.14 km
At 1.286 hours, the car reverses direction. The van is (108 km - 77.14 km) or 30.86 km away.
Add the distances travelled by both vehicles after the car reverses direction at 1.286 hours. The sum will be 30.86 km when they meet, at time of T.
Car Distance + Van Distance = 30.86 km
T(84 km/h) + t(60 km)
They meet when they are 0 km apart, which can be modeled with the following equation:
Van travel Distance - Car Travel Distance = 0 starting at 1.286 hr.
Let t be the time after 1.286 hours that both vehicles meet/collide.
t*(60 km/h) + t(84 km/h) = 30.86 km
t(60+84) = 30.86 km
t(144 km/h) = 30.86 km
t = 0.2143 hr
Total time until the car and van meet is 1.286 hr + 0.2143 hr for a total of 1.50 hours.
=================
a) Time until both vehicles meet is 1.5 hours after starting at noon. That makes it 1:30PM.
b) Average speed of car is 84 km/h
==============
CHECK
Is the ratio of the distance travelled by the car and the van until they meet in the ratio of 7/5?
Car distance is (1.5 hr)(84 km/h) = 126 km
Van distance is (1.5 hr)(60 km/h) = 90.0 km
Ratio is 126/90 or 1.4
Ratio of 7/5 is 1.4
YES
PLEASE HELP
Graph the triangle with the given vertices. Find the length and the slope of each side of the triangle. Then find the coordinates of the midpoint of each side. Is the triangle a right triangle? isosceles? Explain (Assume all variables are positive and m ≠ n)
D (0,n), E(m,n), F(m,0)
Answer:
Triangle DEF is a right, scalene triangle. It is not isosceles, obtuse, acute, or equilateral
Step-by-step explanation:
All we know about m and n are that they are not equal to each other and they are positive. This was given in the problem. See image. Once it is graphed you can see on the graph the lengths of DE and EF. Use Pythagorean theorem to calculate DF. see image.
DE is horizontal and EF is vertical, so you can see their slopes or calculate using a formula. Calculate the slope of DF. Slope is y-y on top of a fraction and x-x on the bottom of the fraction.
Lastly, use midpoint formula to find the midpoints. Average the x's and average the y's to find the x- and y-coordinates of the midpoints. See image.
Finally, DEF is a right triangle. The graph as well as the slopes show us that DE and EF form a right angle. So DEF must be a right triangle (and not obtuse nor acute) We were told that m doesNOT equal n, so the triangle cannot have two equal sides, so it cannot be isosceles (2 equal sides) nor equilateral (3 equal sides) It has 3 different lengths of sides; that is called scalene.
Jamie is ordering cupcakes for an office party. The top three flavors are chocolate/chocolate (x), strawberry/vanilla (y), and peanut butter/chocolate (z). 18 total cupcakes are purchased for $55.75. The chocolate/chocolate are $3 each, the strawberry/vanilla are $2.75 each, and the peanut butter/chocolate are $3.50 each. There are twice as many chocolate/chocolate cupcakes purchased as peanut butter/chocolate cupcakes. How many of each type of cupcake did Jamie purchase
Jamie purchases 4 chocolate (3.57), 7 strawberry/vanilla, and 7 peanut butter cupcakes for an office party.
How to write the given information as an expression or an equation?The steps involved are:
Observe the given data and notice the variable termsUse operators like multiplication or fraction if it consists of terms like twice or thrice or one fourth etc.Use the operators like addition or subtraction (more or less/greater or smaller) in between those variablesSolve those equations for the required values.Calculation:Given that,
Jamie is ordering cupcakes for an office party.
There are three flavors - Chocolate, Strawberry/vanilla, and peanut flavors.
Jamie purchased a total of 18 cupcakes for $55.75
The cost for a single cupcake of each flavor is as follows:
Chocolate - $3
Strawberry - $2.75
Peanut - $3.50
Consider the number of cupcakes of each flavor as x, y, and z respectively.
So, the equations we can write from this data are,
x + y + z = 18 and
3x + 2.75y + 3. 50z = 55.75
But it is given that,
There are twice as many chocolate cupcakes purchased as peanut butter cupcakes.
So, z = 2x
Then the above two equations become,
3x + y = 18 and
10x + 2.75y = 55.75
By solving these two equations we get,
x = 3.57 ≅ 4
y = 7.28 ≅ 7
Since we know that z = 2x,
⇒ z = 2 × 3.57 = 7.14 ≅ 7
So,
There are 4 chocolate, 7 strawberry, and 7 peanut cupcakes.
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Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters. What is the volume of the space filled with tissue paper in the packaging box? 81.84 cubic centimeters 105.84 cubic centimeters 198.264 cubic centimeters 222.264 cubic centimeters
The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters
VolumeVolume if small, Vs = 24 cubic inchesConstant = k
= 2.1³
= 9.261
Volume of large : volume of small = k
Vl / Vs = k
Vl = Vs × k
= 24 × 9.261
= 222.264 cubic inches
Therefore,
Volume of tissue paper = volume of large - volume of small
= 222.264 cubic inches - 24 cubic inches
= 198.261 cubic inches
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8. The heights of female students at North Shore High School are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. About how many students in a random sample of 1000 female students could we expect to have heights less than 167.5 cm
The number of students with heights less than 163 cm should be expected is 12.
According to the statement
The mean of height is 175 cm
and the standard deviation of height is 6 cm.
We use normal distribution here with formula
Z= X - μ /σ
Here X is 167.5 and μ is 175 and σ is 6 cm.
Substitute the values in it then
Z = 167.5 - 175 / 6
Z = -1.25
-1.25 have a p value 0.012
Out of 1000 students:
0.012 x 1000 = 12.
So, The number of students with heights less than 163 cm should be expected is 12.
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A recent article claims that the state of Illinois has low tuition rates for its colleges and universities. Cate decides to research the cost of tuition for different colleges in Illinois. The average tuition in Illinois is $28,950 with a standard deviation of $3,470. Which type of inference test should Cate use
One sample Z Test is used by cate.
According to the statement
The average tuition in Illinois is $28,950 with a standard deviation of $3,470.
Assuming we have a large enough sample, since we are testing one group's mean relative to a hypothesized value, this would be a one-sample z-test.
So, One sample Z Test is used by cate.
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Anna has 3/4 the money Victor has. Victor has 18$ less than Kim they have 386.4 together how much do they each have
Solving a system of equations we can see that:
Anna has $100.47Victor has $133.96Kim has $151.96How to find how much money each one has?
First, let's define the variables:
A = money that Anna has.V = money that Victor has.K = money that Kim has.With the given information we can write 3 equations:
A = (3/4)*V
V = K - $18
A + V + K = $386.4
Then we need to solve a system of equations:
A = (3/4)*V
V = K - $18
A + V + K = $386.4
We can first replace the first equation into the third to get:
(3/4)*V + V + K = $386.4
And rewrite the second to get:
k = V + $18
And replace that in the other equation:
(3/4)*V + V + V + $18 = $386.4
Now we can solve this for V:
V*(1 + 1 + 3/4) = $386.4 - $18
V*(11/4) = $368.40
V = (4/11)*$368.40 = $133.96
Now that we know the value of V, we can replace it in:
K = V + $18 = $133.96 + $18 = $151.96
A = (3/4)*V = (3/4)*$133.96 = $100.47
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Lucas has five buttons in a container. Each button is a different shape. There is a star, an oval, a hexagon, a circle, and a heart. He picks one button, replaces it, and then picks another button.
A) Sample size of compound event = 25
B) New Sample size = 36
What is Compound event?
A compound event is one that has more than one sample point. Simple events are less complicated than compound events. These occurrences entail the possibility of multiple occurrences. One is the probability of all possible outcomes of a compound event.
An event that consists of two or more simple events is called a compound event. Simple events are those that can only have one result, whereas complex events can have a variety of distinct results. Compound events can consist of several independent or dependent occurrences, where the result of one event has no bearing on the likelihood of the other.
Given,
Number of buttons in a container = 5
Lucas picks one button, replaces it and then picks another.
Therefore,
Sample size of the compound event
n = 5[tex]\times[/tex]5
n = 25
Now, one more button is added in the container and in total there are 6 buttons.
Lucas repeats the same process again and hence,
Sample size of the new compound event will be,
n = 6[tex]\times[/tex]6
n = 36
Full Question is - Lucas has five buttons in a container. Each button is a different shape. There is a star, an oval, a hexagon, a circle, and a heart. He picks one button, replaces it, and then picks another button. The sample size for this compound event is ___ Suppose one square-shaped button is added to the container. If Lucas repeats the same picking process, then the sample size would be ____
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Suppose you have 5 riders and 5 horses, and you want to pair them off so that every rider is assigned one horse (and no horse is assigned two riders). How many ways can you do this?
There are 120 ways in which 5 riders and 5 horses can be arranged.
We have,
5 riders and 5 horses,
Now,
We know that,
Now,
Using the arrangement formula of Permutation,
i.e.
The total number of ways [tex]^nN_r = \frac{n!}{(n-r)!}[/tex],
So,
For n = 5,
And,
r = 5
As we have,
n = r,
So,
Now,
Using the above-mentioned formula of arrangement,
i.e.
The total number of ways [tex]^nN_r = \frac{n!}{(n-r)!}[/tex],
Now,
Substituting values,
We get,
[tex]^5N_5 = \frac{5!}{(5-5)!}[/tex]
We get,
The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,
So,
There are 120 ways to arrange horses for riders.
Hence we can say that there are 120 ways in which 5 riders and 5 horses can be arranged.
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Which term describes the set of all possible input values for a function? OA. Range O B. Output O C. Domain O D. Input
Domain refers to the term which best describes the set of all possible input values for a function and is therefore denoted as option C.
What is Domain?These are all the values which go into a function which is defined and is denoted as the sign below:
dom · ( f ).
They are also among the values which form the independent variables in this type of context while on the other hand, the output is referred to as the range.
These set of values are usually inputted into the function to check its acceptability and also retrieve the output gotten from the type of operation given. It is also used to identify the independent variable which are present thereby making it the most appropriate choice.
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