Given,
The weight of candies normally distributed ;
Mean weight of candies = 0.8543 g
Standard deviation, σ = 0.0519 g
Sample of candy came from a packet of 469 candies
Net weight of the packet = 400.3 g
Average weight of the candies in the packet;
[tex]x_{avg} =[/tex] ∑xi/n = 400.3/469 = 0.8535
The population standard deviation (sigma=0.0519 g) is the standard deviation for a confectionery that was chosen at random (sample size n=1).
The z-score can be used to determine the likelihood that an element has a weight greater than 0.8536z = (X - μ) / (σ/√n) = (0.8536 - 0.8535) / (0.0519/√1) = 0.0001/0.0519 = 0.002
P(X > 0.8536) = P(z > 0.002) = 0.4992
A randomly chosen candy has a probability P=0.4992 of weighing at least 0.8536 g.
The z-score needs to be computed if the sample now has n=441 candies and we want to know the likelihood that the mean weight is at least 0.8543 g:z = (X - μ) / (σ/√n) = (0.8543 - 0.8535) / (0.0519/√441) = 0.0008/0.0024 = 0.3288
P(X > 0.8543) = P(z > 0.3288) = 0.37115
A sample of 441 candies chosen at random has a probability P=0.3712 of having an average weight of at least 0.8543 g.
We may determine the likelihood that, for a package of 469 candies and using the mean of 0.8535 g that we previously determined, the average weight is at least 0.8556 g in order to be more certain of the claim that the mean weight is 0.8556 g.z = (X - μ) / (σ/√n) = (0.8556 - 0.8535) / (0.0519/√469) = 0.0021/0.0024 = 0.89
P(X > 0.8556) = P(z > 0.89) = 0.18673
Given that the likelihood is P=0.187, the brand's claim that it delivers the amount promised to customers on the label needs to be reevaluated.
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Felipe the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On
Using system of equations:
Length of each Plan A workout is: 0.5 hour
Length of each Plan B workout is: 1.25 hours
How to Solve a System of Linear Equations?The number of hours that each of the workout plans last can be represented as a system of linear equations. The explanation below shows how to solve this problem using the elimination method.
Let,
x = number of hours for each plan A workout.
y = number of hours for each plan B workout.
Create the system of equations below:
Equation for Friday would be:
3x + 2y = 4 --> equation 1
Equation for Saturday would be:
8x + 4y = 9 --> equation 2
Multiply equation 1 by 4 and equation 2 by 2:
12x + 8y = 16 --> eqn. 3
16x + 8y = 18 --> eqn. 4
Substract eqn. 4 from eqn. 3:
-4x = -2
x = 1/2 = 0.5 [0.5 hours or 1/2 an hour for Plan A]
Substitute x = 0.5 into eqn.1:
3(0.5) + 2y = 4
1.5 + 2y = 4
2y = 4 - 1.5
2y = 2.5
y = 2.5/2
y = 1.25 [1.25 hours for Plan B]
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A new computer cost $890 but is being discounted 15%. Find total cost (include 7% sales tax).
Answer:
$809.455
Step-by-step explanation:
How to find the new cost:
890/100*15
= 133.5
So: 890-133.5
= 756.5
next we find 7% of it (tax):
Which we will find the 7% of it and plus it in
so the new answer is: 809.455
Select all of the segments that must be 9 centimeters long.
Given:
KM=12 cm.
KO=1+KL
[tex]KL=\frac{1}{3}LM[/tex]Since KM=12 cm, we can write
[tex]\begin{gathered} KM=KL+LM \\ KM=\frac{1}{3}LM+LM \\ 12\text{ =}\frac{4}{3}LM \\ LM=\frac{12\times3}{4} \\ LM=9 \end{gathered}[/tex]Therefore, KL can be calculated as,
[tex]\begin{gathered} KL=\frac{1}{3}LM \\ =\frac{1}{3}\times9 \\ =3 \end{gathered}[/tex]Now, KO can be calculated as,
[tex]\begin{gathered} KO=1+KL \\ =1+3 \\ =4 \end{gathered}[/tex]Now, using geometric property,
[tex]KM\times KL=KN\times KO[/tex]Putting the values in the above equation, KN can be calculated as,
[tex]\begin{gathered} 12\times3=KN\times4 \\ KN=\frac{12\times3}{4} \\ KN=9 \end{gathered}[/tex]Now, ON can be calculated as,
[tex]\begin{gathered} ON=KN-KO \\ =9-4 \\ =5 \end{gathered}[/tex]Since LM=9 is a chord longer than MN in the given circle, the length of MN is less than 9.
Therefore, the segments with length 9 are LM and KN.
a circle has a radius 6 in in a central age of 60 what is the measure of the arc length is associated with this angle a 2pie b pie c 6pie d 3 pie
Formula for arc length when the angle is in degrees:
[tex]\text{Arc length = }\frac{\theta}{360}\times2\pi r[/tex]r = radius = 6 in
θ= 60 degrees
[tex]\begin{gathered} \text{Arc length = }\frac{60}{360}\times2\times\pi\times6 \\ \text{arc length = }2\pi\text{ in ches (option A)} \end{gathered}[/tex]10. Seth is analyzing his basketball statistics. The following table shows a probability model for the results of his next two free throws. Outcome Miss both free throws. Is this a valid probability model? True) Yes, this is a valid probability model.False) No, this is not a valid probability model.
Please, give me some minutes to take over your question
_________________________________
I'm working on it
__________________________
a probability model has some features
Events (This part is ok, the probabilities are between 0 - 1 )
1) p1 = 0.2
2) p2 = 0.5
3) p3 = 0.1
____________________
The sample space is not 1 because p1+p2+p3 = 0.8
______________________________________
Answer
FALSE. No, this is not a valid probability model
Consider the function given by the graph. What are
these values?
f(-2)=
f(0) =
f(4) =
The values of the function given by the graph are:
f(-2 ) = 2
f(0) = 3
f(4) = -1
The graph depicts an inequality equation with discontinuities. Points of discontinuity are breaks in the graph caused by an undefined point when the f(x) function is substituted with an x point that is not part of the solution. Looking at the graph of the provided function f(x), we can clearly see that the function f(x) increases in the interval (-∞ ,0] and subsequently decreases in the interval (0,∞).Furthermore, the function terminates at x=0.
(Because there is a gap in the graph and the function's left and right-hand limits are not equal at x=0)
So from the graph, we can determine the values of the functions as,
f(-2 ) =2
f(0) = 3
f(4) = -1
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Answer:
f(–2 ) = 2
f(0) = 3
f(4) = -1
Step-by-step explanation: i hope this helps :)
find value of p. help
If the two line segments are parallel to each other, we can establish the following proportion and reach the result.
[tex]\frac{3p}{3p+(2p-5)} =\frac{26}{26+14}[/tex][tex]120p=130p-130[/tex][tex]130=130p-120p[/tex][tex]130=10p[/tex][tex]13=p[/tex]Therefore, our answer is [tex]p=13[/tex].
How do I solve this?
The functions and its domain are a representation of their dependance on one another.
Functionsfunction, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). In the given question, we have two functions and we are required to find the composite of which ever form of the functions as well as the domain of the said function.
[tex]f(x) = \frac{3}{x}, g(x) = 2x + 8;\\(f.g)(x) = \frac{3}{2x + 8}[/tex]
The domain of the function is given as
[tex]domain = (-\infty , -4) U (-4, \infty)\\[/tex]
In the second composition of the function,
[tex](g.f) = \frac{6}{x} + 8\\domain = (-\infty, 0) U (0, \infty)[/tex]
The third composition of function
[tex](f.f) = x\\domain = (-\infty, \infty)[/tex]
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. G(x) is the function defined by the following graph. The graph window is: [-3,5,1] by [-60,80,10]
We are given a function and we are asked the following questions:
Part 1. Evaluate G(-1). The value of G(-1) is the value of the independent variable, that is the vertical axis when the dependent variable is -1, that is the horizontal axis. To find the value we draw a vertical line perpendicular to the horizontal at the value -1, until we intercept the graph, from there we draw a vertical line until we intercept the vertical axis. From the graph we see that:
[tex]G(-1)=20[/tex]Part 2. Evaluate G(2). This is the value of the independent variable when the dependent variable is 2. From the graph we see:
[tex]G(2)=-10[/tex]Part 3. Determine:
[tex]\frac{G(-1)^3-G(2)^2+4G(-1)}{10}[/tex]Replacing the known values:
[tex]\frac{(20)^3-(-10)^2+4(20)}{10}[/tex]Solving the operations:
[tex]\frac{8000-100+80}{10}=\frac{7980}{10}=798[/tex]Help what would be the answer to this question?
Based on the division of polynomials and logical inference, the missing factor is 10x².
What is the proof for the above answer?Note that the result of:
[15x³ - 22x² + (?)] / (5x-4) = 3x²
This means that
3x² * (5x-4) = [15x³ - 22x² + (?)] .............................1
But
3x² * (5x-4) = 15x³ - 12x²
By reverse calculation, therefore,
We state:
-22x² + (?) = - 12x² [Assume for a moment that x² is eliminated]
-22 + (?) = -12
(?) = -12 +22, Hence
(?) = 10x²
Thus,
[15x³ - 22x² + 10X²) ] / (5x-4) = 3x² .........................................2
Proof:
15x³ - 22x² + 10x² ...................................................................3
= 15x³ - 12x²
Taking common factors:
15x³ - 12x² ⇒ 3(5x³-4x²)
Find one factor
3x² (5x-4) .....................................................................................4
Recall that the problem states that equation 3 / (5x-4) = 3x²
If 15x³ - 22x² + 10x² when simplified =
3x² (5x-4)
Then
15x³ - 22x² + 10x²/ (5x-4) = 3x² (5x-4)/(5x-4)
= 3x²
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3(x + 2) = 3x + 2
Show your work
three dice are tossed. what is the probability of rolling 3 different numbers?
Given:Three dice are tossed.
To find: Probability of rolling 3 different numbers.
Let E be the event of getting same number on three dice.
So,the favorable cases for E will be
(1,1,1) , (2,2,2) , (3,3,3), (4,4,4), (5,5,5) , (6,6,6).
So, the number of favorable cases=6
Now,the total number of cases for E will be
[tex]6\times6\times6[/tex]Since each dice has 6 numbers so three dice will have these number of cases.
Now, the probability to have a same number on 3 dice will be
[tex]P(E)=\frac{\text{Number of favorable cases}}{\text{Number of cases}}\text{ }[/tex][tex]\begin{gathered} P(E)=\frac{6}{6\times6\times6} \\ =\frac{1}{36} \end{gathered}[/tex]Now, probability of rolling 3 different numbers is
[tex]P(nu\text{mbers are different on thr}ee\text{ dice)}=1-P(E)[/tex][tex]\begin{gathered} =1-\frac{1}{36} \\ =\frac{30}{36} \\ =\frac{15}{18} \end{gathered}[/tex]Hence, the probability of rolling three different numbers is
[tex]\frac{15}{18}[/tex]A U-Haul moving truck covered a total distance of 6223 kilometers averaging a speed of 47 km/h in slow moving traffic and 87 km/h in fast moving traffic. The journey took 89 hours. How many hours did the U-Haul moving truck spend in slow moving traffic?
1. **Graph y = 12x + 3 2. ** y = -3x + 4 y 9 T 구 8 16 5 다 2 1 19 18 454 - 6 3-2 1 6 a x 대 - 2 1 2 6 B 9 x 1 0 2 3 10 . -6. R bo 를
Answer:
Graphing the points we have;
Above is the graph of the given equation showing the derived points.
Explanation:
Given the equation;
[tex]y=|2x|+3[/tex]To plot the graph we need to calculate the corresponding values of x and y at each point.
Let us calculate the values of y for x = -4,-2,0,2, and 4;
[tex]\begin{gathered} y=|2x|+3 \\ at\text{ x=-4;} \\ y=|2\times-4|+3 \\ y=8+3 \\ y=11 \\ (-4,11) \end{gathered}[/tex][tex]\begin{gathered} at\text{ x=-2} \\ y=|2\times-2|+3 \\ y=4+3 \\ y=7 \\ (-2,7) \end{gathered}[/tex][tex]\begin{gathered} at\text{ x=0;} \\ y=|2\times0|+3 \\ y=3 \\ (0,3) \end{gathered}[/tex][tex]\begin{gathered} at\text{ x=2;} \\ y=|2\times2|+3 \\ y=4+3 \\ y=7 \\ (2,7) \end{gathered}[/tex][tex]\begin{gathered} at\text{ x=4;} \\ y=|2\times4|+3 \\ y=8+3 \\ y=11 \\ (4,11) \end{gathered}[/tex]Therefore, Graphing the points we have;
Above is the graph of the given equation showing the derived points.
Amber solved the equation −2=10−3(2+6).
Match the property with each of Amber's steps for solving the equation.
The property use to solve the equation is as follows:
Distributive propertyCombine like termsAdditive property of equalityDivision property of equalityHow to solve equations?The equation can be solved as follows:
−2a = 10 − 3(2a + 6)
Using distributive property,
−2a = 10 − 3(2a + 6)
- 2a = 10 - 6a - 18
According to distributive law, multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.
Combine like terms
- 2a = 10 - 6a - 18
- 2a = -6a - 8
Using additive property of equality, we will add 6a to both sides of the equation.
The additive property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.
- 2a = -6a - 8
- 2a + 6a = -6a + 6a - 8
4a = - 8
using division property of equality, we will divide both sides of the equation by 4.
The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal.
4a = - 8
4a / 4 = -8 / 4
a = - 2
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I need help with this question for my computer class
SOLUTION:
Case: Spreadsheet calculations
Method:
Some common signs
'+' does sum
'-' does difference
'*' does the product
'/' does division
Hence
C7-B6 does the difference for cells C7 and B6
Final answer: Option (D)
C7-B6
Find the volume of the cylinder. Either enter an exact answer in terms of or use 3.14 for 4 units 3 Stuck? Watch a video or use a hint.
the volume of a cilinder is:
[tex]V=\pi r^2h[/tex]So we can replace the radius and the high so:
[tex]\begin{gathered} V=\pi6^24 \\ V=36\cdot4\cdot\pi \\ V=144\pi \end{gathered}[/tex]Now we can replace pi by 3.14 so:
[tex]undefined[/tex]For what value of t does t / 4 / 16 = 1/16?
Answer: t = 4
Isolating a variable: rearranging an equation so that the variable is on its own
A value of t that satisfies the equation must be foundA variable can be isolated by performing opposite operationsCalculations:
[tex]\frac{\frac{t}{4} }{16} = \frac{1}{16}[/tex]
[tex]\frac{t}{4}= 16/16[/tex] - calculated by multiplying 1/16 by 16
[tex]t= 16/16[/tex] × [tex]4[/tex]
[tex]t= \frac{64}{16}[/tex]
[tex]t=4[/tex] - simplified answer
Which expression is equivalent to the quantity five raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power? three raised to the third power divided by five raised to the fourth power negative three raised to the third power divided by five raised to the fourth power five raised to the fourth power divided by three raised to the tenth power negative five raised to the fourth power divided by three raised to the tenth power
Answer:
(c) five raised to the fourth power divided by three raised to the tenth power
Step-by-step explanation:
You want the simplified version of the quantity five raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power.
Rules of exponentsThe relevant rules of exponents are ...
(ab)^c = (a^c)(b^c)
a^-b = 1/a^b
(a^b)^c = a^(bc)
ApplicationThe given expression can be simplified as follows:
[tex](5^{-2}3^5)^{-2}=5^{(-2)(-2)}3^{(5)(-2)}=5^43^{-10}=\boxed{\dfrac{5^4}{3^{10}}}[/tex]
__
Additional comment
We find math expressions easier to understand when they are written using math notation, instead of words.
I'll give brainliest!
Answer:
The side length, s, of the square is 18
Step-by-step explanation:
The sides can be found by taking the square root of the area.
(Area)^1/2=s, where s = side.
(324)^1/2=18
A circle in the xy-plane has a center at G 3 1 42 3 and a radius that is units long. Which of the 15 following is an equation of the circle?
We are asked to find the equation of a circle on the xy-plane, with center (3/4 , 1/2) and a radius of 3/5 units. For doing so, we remember the general equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h,k) represents the center of the circunference, and r its radius.
In our example, we obtain that,
[tex]\text{Center}=(\frac{3}{4},\frac{1}{2})[/tex]And so,
[tex]\begin{gathered} h=\frac{3}{4},k=\frac{1}{2} \\ r=\frac{3}{5} \end{gathered}[/tex]Applying the above formula, we get that the equation of the circle will be:
[tex](x-\frac{3}{4})^2+(y-\frac{1}{2})^2=(\frac{3}{5})^2[/tex]This is:
[tex]\mleft(x-\frac{3}{4}\mright)^2+\mleft(y-\frac{1}{2}\mright)^2=\frac{9}{25}[/tex]i don't know how to setup the equation and neither getting the answer, please help, i only need question 4 btw
The sum of exterior angles of a regular polygon is 360 degree.
Determine the measure of last exterior angle of a regular pentagon.
[tex]\begin{gathered} 52+87+90+43+x=360 \\ x=360-272 \\ =88 \end{gathered}[/tex]So measure of last angle of a regular pentagon is 88 degree.
5. Graph the function f (x) = 3sin (2x) + 1 Be sure to identify the midline, period, and amplitude.Period= pi Amplitude= 3 Midline = -1 Need help with graphing
Answer:
[tex]\begin{gathered} \text{Amplitude}=3 \\ \text{Midline is at: }y=1 \\ \text{Period}=\pi \end{gathered}[/tex]we can now graph the function as;
Explanation:
Given the equation;
[tex]f(x)=3\sin (2x)+1[/tex]Firstly, to derive the period, Amphitude and midline, let us compare to the general form;
[tex]\begin{gathered} f(x)=A\sin (Bx+C)+D \\ A=\text{Amplitude} \\ D=\text{midline} \\ \text{ since C=0 for the given equation;} \\ \text{Period=}\frac{2\pi}{B} \end{gathered}[/tex]From the given equation;
[tex]\begin{gathered} A=3 \\ D=1 \\ B=2 \\ \therefore \\ \text{Amplitude}=3 \\ \text{Midline is at: }y=1 \\ \text{Period}=\frac{2\pi}{2} \\ \text{Period}=\pi \end{gathered}[/tex]With the above characteristics we can now graph the function as;
I don't remember what an isosceles triangle is
An isosceles triangle is a triangle which has two of its sides with the same length
What statement is true? 3/7 is greater than 0.516 3/7 is less than 0.516 3/7 equal 0.516
ANSWER
3/7 is less than 0.516
EXPLANATION
Wwe want to compare the two numbers 3/7 and 0.516.
Let us convert 3/7 to decimal so we can compare properly:
3/7 = 0.429
As we can see:
0.429 is less than 0.516
So, 3/7 is less than 0.516
HELP ASPP PLEASE SHOW UR WORK
Answer: 7
Step-by-step explanation:
1) Set up an equation. Let x be the number of hours he works.
[tex]400\leq 64x[/tex]
2) Solve the equation
(<= mean less or equal to)
400/64 <= x
6.25 <= x
3) Solve the problem
We need to round up 6.25 as 6.25 is not on the list. Since the number has to be greater than 6.25, the next option is 7.
What is the value of the number in the tenths place?6.748O A. 0.7B. 0.04C. 0.07D. 0.6
Answer:
Choice A. 0.7
Explanation:
The place value of the numbers is given below
T
Match each of the following expressions to its meaning in the context of this situation.Question is in picture
Step 1
Given;
[tex]\begin{gathered} Pizza\text{ store charges 6\% sales tax and \$5 on delivery} \\ Functions\text{ that represent the situation are;} \\ f(a)=1.06a \\ g(b)=b+5 \end{gathered}[/tex]Step 2
Match each of the following expressions to its meaning in the context of this situation.
[tex]undefined[/tex]Stella has 35 rocks in her rock collection. Each month she will add 15 rocks to the collection. Which equation can be used to find y, the total number of rocks in Stella's collection after x months? A) y = 35x + 15 B) y = 15x - 35 c) y = 35x - 15 D) y = 15x +35
Answer:
A
Step-by-step explanation:
y = 35 + 15x
A
:]
Look at the photo i placed below for further info
In order to find the value of x, we need to remember that the sum of the interior angles of a triangle is 180°
the equation to find x is
[tex]61+29+x=180[/tex]we need to isolate the x
[tex]\begin{gathered} x=180-61-29 \\ x=90 \end{gathered}[/tex]the answer is c x=90°