Answer:
a. -1.60377
b. 0.25451
c. 0.344
d. Option b) 78th
Step-by-step explanation:
The number of pieces in a regular bag of Skittles is approximately normally distributed with a mean of 38.4 and a standard deviation of 2.12.
a)What is the z-score value of a randomly selected bag of Skittles that has 35 Skittles? a) 1.62 b) -1.62 c) 3.40 d) -3.40 e)1.303.
The formula for calculating a z-score is is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
z = 35 - 38.4/2.12
= -1.60377
Option b) -1.62 is correct
b) What is the probability that a randomly selected bag of Skittles has at least 37 Skittles? a) .152 b) .247 c) .253 d).747e).7534. .
z = (x-μ)/σ
Mean of 38.4 and a standard deviation of 2.12.
z = (37 - 38.4)/2.12
= -0.66038
P-value from Z-Table:
P(x<37) = 0.25451
The probability that a randomly selected bag of Skittles has at least 37 Skittles is 0.25451
Option c) .253 is.correct
c) What is the probability that a randomly selected bag of Skittles has between 39 and 42 Skittles? a) .112 b) .232 c) .344 d).457 e).6125.
z = (x-μ)/σ
Mean of 38.4 and a standard deviation of 2.12.
For 39 Skittles
z = (39 - 38.4)/2.12
= 0.28302
Probability value from Z-Table:
P(x = 39) = 0.61142
For 42 Skittles
z = (42 - 38.4)/2.12
= 1.69811
Probability value from Z-Table:
P(x = 42) = 0.95526
The probability that a randomly selected bag of Skittles has between 39 and 42 Skittles is:
P(x = 42) - P(x = 39
0.95526 - 0.61142
0.34384
= 0.344
Option c is.correct
d) What is the percentile rank of a randomly selected bag of Skittles that has 40 Skittles in it? a)82nd b) 78th c) 75th d)25th e)22nd
z = (x-μ)/σ
Mean of 38.4 and a standard deviation of 2.12.
z = (40 - 38.4)/2.12
= 0.75472
P-value from Z-Table:
P(x = 40) = 0.77479
Converting to percentage = 0.77479× 100
= 77. 479%
≈ 77.5
Percentile rank = 78th
Calculate the monthly payment for a loan of $7,500 with an 11% interest rate compounded monthly over a period of 5 years.
Answer:
Option b - $163.07
Step-by-step explanation:
Given : A loan of $7,500 with an 11% interest rate compounded monthly over a period of 5 years.
To find : Monthly payment
Solution : Formula to find monthly payment
Monthly Payment = Amount / Discount factor
Discount factor
where ,
Amount = $7500
Rate= 11%=0.11
Time = 5 years
Now, put i and n in Discount factor ,
Monthly payment,
Therefore, Option b is correct monthly payment = $163.07
Answer:
The answer is $163.07
Step-by-step explanation:
To find the monthly payment:
[tex]i = \frac{0.11}{12} = 0.0091[/tex]
Time = 5 years
5 x 12 = 60
Discount factor
[tex]D = \frac{1-(1 + i) -^{n}}i[/tex]
[tex]D = \frac{1 - (1+ 0.009)-^{60} }{0.009} \\[/tex]
[tex]D = \frac{0.421}{0.009} = 46.77[/tex]
Monthly payment
[tex]\frac{7500}{46.77} = $163.07[/tex]
For which values of c does the quadratic equation x^2-2x+c=0 Two roots of opposite signs
Answer:
-2
Step-by-step explanation:
The value of c is -4, therefore the additive inverse should be added to get the answer 0
The roots of the quadratic equation x² – 2x + c = 0 are a and –b. Then the value of c is a² – 2a.
What is a quadratic equation?It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
For which values of c does the quadratic equation
x² – 2x + c = 0 ...1
Two roots of opposite signs
Let the two roots of the opposite signs be a and –b
x = a, –b
Then we have factorized the equation,
(x + b)(x – a) = 0
On solving, we have
x² + (b – a)x – ab = 0 ...2
In comparing equation 2 with equation 1, we have
⇒ b – a = –2
⇒ b = –2 + a
and
⇒ c = a(a – 2) = a² – 2a
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
The temperature inside my refrigerator is about 40 ◦Celsius. If I place a balloon in my fridge that initially has a temperature of 220 °C and a volume of 0.5 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator? Using Charles' Law
Answer:
The volume of the balloon when it is fully cooled by my refrigerator is
2.75liters
Step-by-step explanation:
we are expected to apply Charles law in this problem and solve for the final volume V2
the expression for Charles law is give as
V1/T1=V2/T2
given data
V1, first volume = 0.5 liters
V2, second volume =?
T1, first temperature = 40 ◦Celsius.
T2, second temperature =220 °C
applying the formula we have
0.5/40=V2/220
V2=(0.5*220)*40
V2=110/40
V2=2.75liters
Three straight lines are shown in the diagram. Work out the sizes of angles a,b and c.
15 points to whoever gets this by the way.
Answer:
b = 100°
should be the answer
What is the equation written in vertex form of a parabola with a vertex of (–1, 8) that passes through (1, 0)?
Answer:
y = -2(x + 1)^2 + 8
Step-by-step explanation:
The equation of a parabola can be written in the form;
y = a(x-h)^2 + k
where a is the multiplier (h,k) is the vertex
so h = -1 and k = 8
Plug in these values
y = a(x + 1)^2 + 8
So to get the value of a, we use the point where the parabola passes through which is the point (1,0)
Simply substitute the values of x and y
0 = a(1 + 1)^2 + 8
0 = a(2)^2 + 8
-8 = 4a
a = -8/4
a = -2
So therefore the equation of the parabola is ;
y = -2(x + 1)^2 + 8
The required equation of parabola with given vertex and point of passing is [tex]y=-2(x+1)^{2}+8[/tex].
Given data:
The vertex of parabola is, (-1, 8).
The vertex is passing through (1, 0).
We know that standard equation parabola is,
[tex]y=a(x-h)^{2}+k[/tex]
Here, a is any multiplier, h and k are the vertices.
From the given problem,
h = -1
k = 8
So substituting the values as,
[tex]y=a(x-(-1))^{2}+8\\y=a(x+1)^{2}+8[/tex]..............................................(1)
To obtain the value of a, we use the point where the parabola passes through which is the point (1,0). Here, x = 1 and y =0.
So,
[tex]0=a(1+1)^{2}+8\\\\a = -2[/tex]
Substitute the value of a in equation (1) as,
[tex]y=(-2)(x+1)^{2}+8\\\\y=-2(x+1)^{2}+8[/tex]
Thus, the required equation of parabola is [tex]y=-2(x+1)^{2}+8[/tex].
learn more about the parabola here:
https://brainly.com/question/4074088
Two angles are complementary. One angle measures 28 What is the measure of the other angle?
the sum of two complementary angles is 90°
so 28 + ? = 90
? = 62°
here'
complementry angle means those whose sum is 90
here one angle is given so,
another angle =90-28
that is 72.ans
532^7•532^-8•532^3
How do I do this it’s hard
Answer:
283024
Step-by-step explanation:
First do 532^7
The answer is 12060947473224100000
Next, do 532^-8
The answer is 1/6416424055755230000000
Multiply that number by the first number
(I don't want to type that all out again)
The answer is 1/532
Now, do the last problem. 532^3
The answer is 150568768
Multiply that number by 1/532
The answer is 283024
Hope I helped :)
Please consider Brainliest :)
(it took me so long to type that)
what is the answer???????????
Answer:
Step-by-step explanation:
First we make the denominators the same:
2/3 = 10/15
2/5 = 6/15
Ratio: 6/15 : 10/15
Have a great day!!
Please rate and mark brainliest!!
Find the product. −3y2(−5y3 + y − 6)
please help me pls ease
Answer:
8
Step-by-step explanation:
x = -2
the y to (-2,y) is 8
Please help me find the y-intercept and slope from these two-word problems. ANd tell me if they're proportional and negative or not.
Answer:
for the 1st one, m=10 and b=2 because from the word problem it says it starts at 10 which would be 10 on the y axis being where the line would pass through and spending 2 a week would be the slope because he is losing 2 per week its a negative slope so y=10x-2.
for the second one m=48 and b=44 its just like the last one but with different numbers but comment if you want me to explain it but the answer is y=48x-44.
HELP i need help quickly please
Answer:
c
Step-by-step explanation:
Part D In the scale drawing, what will the length of the west side of the backyard be?
NEED HELP ASAP WILL GIVE BRAINIST TO BEST AWNSER
Answer: answer witten in the picture attached to this......
Which linear inequality is represented by the graph?
y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y 3x − 1
Answer:
B
Step-by-step explanation:
Answer: B or y ≥ 1/3x − 1
Step-by-step explanation:
Got it right Edge 2020
Hello Guys, I really need help with these questions. Here they are.
Solve each absolute value inequality and show its solution set.
(a) |x|<7
(b) |x+3|<9
(c) |y-8|>11
(g) |3x-1| greater or equal to 18
|4y+3| less than or equal to 13
Please help me with these. WIll give you 20 pts. I will award brainly for the best answer! Make the answers in numbers (inequalities)
Answer:
a.[tex]-7 < x < 7[/tex]
b.[tex]-12 < x < 6[/tex]
c. Two answers are: y < -3 or y > 19
d. Two answers are x ≤ -17/3 or x ≥ 19/3
e. -4 ≤ y ≤ 5/2
Step-by-step explanation:
Given the following questions:
Question one:
[tex]|x| < 7[/tex]
x is less than 7
[tex]=-7 < x < 7[/tex]
Question two:
[tex]|x+3| < 9[/tex]
[tex]x+3 > -9[/tex]
[tex]3-3=0[/tex]
[tex]-9+-3=-12[/tex]
[tex]x > -12[/tex]
[tex]x+3 < 9[/tex]
[tex]3-3=0[/tex]
[tex]9-3=6[/tex]
[tex]x < 6[/tex]
x is greater than -12, while less than 6
[tex]-12 < x < 6[/tex]
Question three:
[tex]|y-8| > 11[/tex]
[tex]y-8 < -11[/tex]
[tex]-8+8=0[/tex]
[tex]-11+8=-3[/tex]
[tex]y < -3[/tex]
[tex]y-8 > 11[/tex]
[tex]-8+8=0[/tex]
[tex]11+8=19[/tex]
[tex]y > 19[/tex]
Two answers are: y < -3 or y > 19
Question four:
|3x - 1| ≥ 18
3x - 1 ≤ -18
-1 + 1 = 0
-18 + 1 = -17
3x ≤ -17
x ≤ -17/3
3x - 1 ≥ 18
-1 + 1 = 0
18 + 1 = 19
3x ≥ 19
x ≥ 19/3
Two answers are: x ≤ -17/3 or x ≥ 19/3
Question five:
|4y + 3| ≤ 13
|4y + 3| ≤ 13 = -13 ≤ 4y + 3 ≤ 13
-13 ≤ 4y + 3 ≤ 13
4y + 3 ≥ -13
3 - 3 = 0
-13 + - 3 = -16
4y ≥ -16
4 ÷ - 16 = -4
y ≥ -4
4y + 3 ≤ 13
3 + -3 = 0
13 - 3 = 10
4y ≤ 10 = 10/4 ÷ 2 = 5/2
y ≤ 5/2
-4 ≤ y ≤ 5/2
Hope this helps.
I don't understand at all of how to do this
Answer:
17
Step-by-step explanation:
5x2=10
8 1/2x2=17
Foster is centering a photo that is 9 1/2 inches wide on a scrapbook page that is 14 inches wide. How far from each side of the page should he put the picture? Enter your answer as a mixed number.
Step-by-step explanation:
Given that he dimension is
9 1/2 inches wide
and 14 inches wide.
half way from 9.5 inches is
4.75in
half way from 14 inches is
7in
Therefore he put the picture at 4.75in from the top and 7in from the sides
If the ratio of a:b is 4:15 and the ratio of b:c is 5:9, what is the ratio of a:c?
Answer:
Your answer should be 4:9
Step-by-step explanation:
Good luck.
f(x)=1/3x-4 is it linear or exponential?
Answer:
Linear
Step-by-step explanation:
since the x value has no exponent to it, and is simply on its own, it is linear
Generalize the patterns you noticed in part D to create a rule or identity to describe those patterns. For example, if you notice that every time you multiply a negative number by another negative number the result is positive, we can generalize this by saying (-a)(-b) = c, where a, b, and c are all positive real numbers.
I know it is probably to late for your answer but if you are on Solving and Reasoning with Complex Numbers: Tutorial in Edmentum, then the answer for part D on the first lesson activity is this word for word.
This equation generalizes the patterns seen in part D, where a and b represent real numbers:
(a + bi)(a − bi) = a2 + b2.
Hope this helps good luck
When simplifying expressions that involve many exponent properties, how do you decide what to do first?
first (...), after √ and squares from left to right then from left to right . and : and lastly + and -
What is the additive inverse of the number 1.6?
A. -1.6
B. 0
C. 1
D. 6.1
Answer:
-1.6
Step-by-step explanation:
Because the additive inverse of any positive number is it's negative number
If f(x) = 5x +5, which of the following is the inverse of f(x)?
=
=
(x)
3
(x+)
O A. F'(x) = 5*55
-(
O B. F'(x) = 36445)
f-
O c. f'(x) = 5(x+5)
-=
O D. +++(x) = 34,553
f-
5
3
(-)
Answer: D
Step-by-step explanation:
what is the answer for thiss please helpp
3-2x<1
Answer:
x > 1
Step-by-step explanation:
3 - 2x < 1
- 2x < 1 - 3
- 2x < - 2
Divide - 2 on both sides,
- 2x / - 2 > - 2 / - 2
x > 1
Answer:
x>1
Step-by-step explanation:
3-2x<1-2x<1-3-2x<-2x>-2/-2[Sign alter because dividing by negative number]Hence, x>1
There are 300 light bulbs lined up in a row in a long
room. Each bulb has its own switch and is currently
switched off. Each bulb is numbered consecutively from
1 to 270. You first flip every switch. You then flip the
switch on every second bulb(turning off 2, 4,6. ). You
then flip the switch on every third bulb (3, 6,. ). This
continues until you have gone through the process 300
times.
And how many of the light bulbs are illuminated now?
Flipping the bulbs is an illustration of sequence and patterns
17 bulbs would remain on.
How to determine the number of bulbs that will be on?The sequence of turning the bulbs off and on, would change the state of the bulbs until the 300th process.
While changing the state of the bulbs, the bulb at the perfect square positions would remain on.
There are 17 perfect square numbers between 1 and 300 (inclusive)
Hence, 17 bulbs would remain on.
Read more about sequence and patterns at:
brainly.com/question/26698448
Which function BEST represents the graph?
Answer:
The last one
Step-by-step explanation:
K so first look at y intercept which is +5, so we eliminate A and C, then the graph opens up so the b in ax+bx+c has to be positive which is D
the point ( 0 ; 5 ) in on the curve
so f(0) = 5
choice between :
x² - 2x + 5 or x² + 2x + 5 then :
we have the point (1 ; 4)
with x² - 2x + 5
f(1) = 1² - 2*1 + 5 = 1 - 2 + 5 = 4
so it's correct
=> x² - 2x + 5 is the right one
solve the simultanious equasion
8x+3y=45
2x+3y=27
pls pls pls help
Answer:
[tex]x=3,\:y=7[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}8x+3y=45\\ 2x+3y=27\end{bmatrix}[/tex]
[tex]\mathrm{Substitute\:}x=\frac{45-3y}{8}[/tex]
[tex]\begin{bmatrix}2\cdot \frac{45-3y}{8}+3y=27\end{bmatrix}[/tex]
[tex]\begin{bmatrix}\frac{45+9y}{4}=27\end{bmatrix}[/tex]
[tex]y=7[/tex]
[tex]\mathrm{For\:}x=\frac{45-3y}{8}[/tex]
[tex]\mathrm{Substitute\:}y=7[/tex]
[tex]x=\frac{45-3\cdot \:7}{8}[/tex]
[tex]x=3[/tex]
[tex]\mathrm{The\:solutions\:are}:[/tex]
[tex]x=3,\:y=7[/tex]
i need help with this equation its confusing ASAP
Answer:
multiply both sides by 3
Step-by-step explanation:
i would multiply 3 on both sides to cancel the fraction out so i dont have to work with fractions
Answer:
multiply both 3 sides
Step-by-step explanation:
real simple m
What is the value of x?
x=32 degrees
Step-by-step explanation:
Angles in equilateral triangles are equal, each angle is 60 degrees
2x-4 =60
+4
2x = 64
÷2
x = 32
Also, y will be 12 (12x5=60)
Hope this helps!
John sells frozen fruit bars at a stand in a park during the summer months. He records the average weekly temperature and number of frozen fruit bars sold for 6 weeks. A 2-column table with 6 rows. The first column is labeled temperature (degrees Fahrenheit) with entries 67, 71, 76, 76, 82, 87. The second column is labeled fruit bars sold with entries 50, 54, 63, 65, 65, 100. What type of correlation exists between the temperature and the number of fruit bars sold? What is the real-world meaning of the slope of the line of best fit for the given scenario? There are approximately more fruit bars sold for every degree(s) the temperature rises.
The correlation that exists between the temperature and the number of fruits sold is positive but is almost negligible.
What is the correlation coefficient?The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at all, therefore, independent variable.
We know that the correlation coefficient is given by the formula,
[tex]r =\dfrac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]
r = correlation coefficient
[tex]x_{i}[/tex] = values of the x-variable in a sample
[tex]\bar{x}[/tex] = mean of the values of the x-variable
[tex]y_{i}[/tex] = values of the y-variable in a sample
[tex]\bar{y}[/tex] = mean of the values of the y-variable
Calculate the value of [tex](x_i-\bar{x})(y_i-\bar{y}),\ (x_i-\bar{x})^2,{ \rm and}\ (y_i-\bar{y})^2[/tex] each separately, and then find the sum of them as shown below, therefore, the formula can be written as,
[tex]r =\dfrac{571.5}{261.5\times 1566.833333}= 0.0014[/tex]
Hence, the correlation that exists between the temperature and the number of fruits sold is positive but is almost negligible.
Learn more about Correlation Coefficients:
https://brainly.com/question/15353989
Answer:
1. positive
2. 2.2
3. 1
Step-by-step explanation: