Using the normal distribution, the percentages are given as follows:
a. 9.18%.
b. 97.72%.
c. 50%.
d. 4.27%.
e. 0.13%.
f. 59.29%.
g. 2.46%.
h. 50%.
i. 50%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 247, \sigma = 60[/tex]
For item a, the proportion is the p-value of Z when X = 167, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (167 - 247)/60
Z = -1.33.
Z = -1.33 has a p-value of 0.0918.
Hence the percentage is of 9.18%.
For item b, the proportion is the p-value of Z when X = 367, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (367 - 247)/60
Z = 2.
Z = 2 has a p-value of 0.9772.
Hence the percentage is of 97.72%.
For item c, the proportion is one subtracted by the p-value of Z when X = 247, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (247 - 247)/60
Z = 0.
Z = 0 has a p-value of 0.5.
1 - 0.5 = 0.5.
Hence the percentage is of 50%.
For item d, the proportion is one subtracted by the p-value of Z when X = 350, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (350 - 247)/60
Z = 1.72
Z = 1.72 has a p-value of 0.9573.
1 - 0.9573 = 0.0427.
Hence the percentage is of 4.27%.
For item e, the proportion is the p-value of Z when X = 67, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (67 - 247)/60
Z = -3.
Z = -3 has a p-value of 0.0013.
Hence the percentage is of 0.13%.
For item f, the proportion is the p-value of Z when X = 300 subtracted by the p-value of Z when X = 200, hence:
X = 300:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (300 - 247)/60
Z = 0.88.
Z = 0.88 has a p-value of 0.8106.
X = 200:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (200 - 247)/60
Z = -0.78.
Z = -0.78 has a p-value of 0.2177.
0.8106 - 0.2177 = 0.5929.
Hence the percentage is of 59.29%.
For item g, the proportion is the p-value of Z when X = 400 subtracted by the p-value of Z when X = 360, hence:
X = 400:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (400 - 247)/60
Z = 2.55.
Z = 2.55 has a p-value of 0.9946.
X = 360:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (360 - 247)/60
Z = 1.88.
Z = 1.88 has a p-value of 0.97.
0.9946 - 0.97 = 0.0246.
Hence the percentage is of 2.46%.
For items h and i, the distribution is symmetric and the mean and the median are equal, hence both percentages are 50%.
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The lengths of the three sides of a triangle (in centimeters) are consecutive odd
integers. If the perimeter is 45 centimeters, find the value of the shortest of the three
side lengths.
Answer:
13, 15,17
Step-by-step explanation:
Let x = the first number
Let x + 2 = the second number
Let x + 4 = the third number
Consecutive means in order like 1,2,3 or 20,21,22. Consecutive odd means that you want three numbers in order that are odd. Each number would be 2 more than the number before. For example 5 + 2 = 7. We would have to add 4 to 5 to find the next consecutive odd number.
x + (x + 2) + (x +4) = 45 I put the numbers in parentheses so you could see the first number plus the second number plus the third number equals 45
x + x+ 2 + x+ 4 = 45 Combine like terms
3x + 6 = 45 Subtract 6 from both sides of the equation.
3x = 39 Divide both sides by 3
x = 13
Add 2 to that to get the next odd number.
Add 4 to 13 to get the third odd number.
Answer: 13 cm
Step-by-step explanation:
Let the value of the shortest of the three side lengths is x.
Since the three sides of a triangle are consecutive odd
integers, hence: x, x+2, x+4.
Thus,
[tex]P=x+(x+2)+(x+4)\\45=x+x+2+x+4\\45=3x+6\\45-6=3x+6-6\\39=3x\\[/tex]
Divide both parts of the equation by 3:
[tex]13\ cm=x[/tex]
What is the product of −2 1/4 and 2 1/2?
help me
The problem is asking for the product, meaning we need to multiply.
-2 1/4 * 2 1/2
To make multiplying easier, we can convert the mixed numbers into improper fractions.
2 * 4 = 8, + 1 = 9/4
2 * 2 = 4, + 1 = 5/2
Now, we have this:
-9/4 * 5/2
Since the denominators are different, we can find the least common multiple of the denominators to make them the same. In this case, the least common multiple of 4 and 2 is 4.
-9/4 * 1 = -9/4
5/2 * 2 = 10/4
Now, we have this:
-9/4 * 10/4
We can now multiply!
-9 * 10 = -90
/4 * /4 = /16
= -90/16
You can simply the improper fraction if you'd like.
-90 / 16 = -5.625
So, our answer is -90/16, or -5.625.
I need help with the delta math order signed number (level 2) Drag the numbers below to put them in order from least to greatest
The numbers ordered from least to greatest are- 2.14, 2.2, 2.221, 2.276, 2.26, 2.291.
Here, we are given 6 numbers-
2.2, 2.276, 2.291, 2.14, 2.26, 2.221
Now, we can add as many zeroes as we want after the decimal, it does not change the value of the number.
Thus, let us make all the numbers 3 digit decimal numbers
2.200, 2.276, 2.291, 2.140, 2.260, 2.221
Here, all the numbers have 2 in the units place, so we just need to compare the decimals
The first digit after decimal is 2 in all the numbers except 2.140, thus it is the smallest.
Then, the second digit after decimal is 0 in 2.200, thus it is the next smallest number.
By similar logic, looking at the second digit after the decimal only we can arrange the remaining numbers as 2.221, 2.276, 2.260, 2.291.
Thus, the numbers ordered from least to greatest are- 2.14, 2.2, 2.221, 2.276, 2.26, 2.291.
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Your question was incomplete. Please check for full content below-
Drag the numbers below to put them in order from least to greatest
2.2, 2.276, 2.291, 2.14, 2.26, 2.221
keiko's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs keiko $5.35 per pound, and type b coffee costs $4.05 per pound. this month, keiko made 166 pounds of the blend, for a total cost of . how many pounds of type b coffee did she use?
Keiko used 83.5 pounds of type A coffee and 82.5 pounds of type B coffee in the blend.
What exactly are algebraic expressions?
An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression
Given:
Type A coffee cost $5.35 per pound
Type B Coffee cost $4.05 per pound
Keiko made total 166 pound of the blend of $780.85
Therefore,
[tex]5.35x + 4.05y = 780.85 \;\;\;\;\; -------equation (1)[/tex]
[tex]x + y = 166 \;\;\;\; ---------equation (2)[/tex]
simplify the equation (2),
[tex]y = 166-x[/tex]
Substitute the value of y in equation (1),
[tex]5.35x + 4.05 (166-x) = 780.85[/tex]
[tex]5.35x + 672.3 - 4.05x = 780.85[/tex]
[tex]5.35x-4.05x=780.85-672.3[/tex]
[tex]1.3x=108.55[/tex]
Therefore,
[tex]Total\;pound\;of\;type\;A\;coffee\;is,\;x=83.5\;pounds[/tex]
Substitute the value of x in equation (2),
[tex]y=166-83.5[/tex]
Therefore,
[tex]Total\;pound\;of\;type\;B\;coffee\;is,\;y=82.5\;pounds[/tex]
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The answer to Gprahing systems of equations
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
PLEASE DONT STEAL MY POINTS AND BEST ANSWER GETS BRAINLEST.
A falcon flies 800,000 meters in 4 hours. Use the formula d = rt, where d represents distance, r represents rate, and t represents time, to answer the following questions. Show your work.
Part A: Rearrange the distance formula, d = rt, to solve for rate. (2 points)
Part B: Find the falcon's rate in meters per hour. (3 points)
Part C: Find the falcon's rate in kilometers per hour. (3 points)
Part D: Which unit, meters, or kilometers, makes more sense to use in this scenario, and why? (2 points)
The answers are :
Part A: r = d/t, Part B: 200,000 meters per hour, Part C: 200 kilometres per hour Part D: Kilometres is more appropriate.
Part A: To rearrange the distance formula for the value of rate, rate will be on Left Hand Side of the equation and other variables will be on Right Hand Side of the equation.
rate = distance/time.
Part B: Rate in meter per hour can be calculated by keeping the values in formula formed in Part A.
Rate = 800,000 ÷ 4
Rate = 200,000 meters per hour.
Part C: To find the rate in kilometres per hour, we will simply convert the calculated rate from meters to kilometres. As per the known fact, 1000 meters = 1 kilometre.
Rate = 200,000 ÷ 1000
Rate = 200 kilometres per hour
Part D: The use of unit kilometre is more appropriate in this problem. This is because the speed is fast and contains many zeroes. Reading and understanding in the form of kilometres is more practical in comparison to meters.
Hence, Part A: r = d/t, Part B: 200,000 meters per hour, Part C: 200 kilometres per hour Part D: Kilometres is more appropriate
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A farmer has 120 bushels of apples to sell at his stand. he sells an average of 16 3/5 bushels each day. represent the total change in the number of bushels he has for sale after 7 days
The total change in the number of bushels he has for sale after 7 days = 116.2
In this question,
A farmer sells an average of 16 3/5 bushels each day.
We write above improper fraction 16 3/5 in proper fraction as 83/5
And the decimal form of given fraction 83/5 is:
83/5 = 16.6
After 7 days, he would sold (16 3/5) × 7 bushels.
We simplify an expression (16 3/5) × 7
(16 3/5) × 7 = 16.6 × 7
= 116.2
As a result, the farmer would have only 120 - 116.2 = 3.8 bushels for sale.
Therefore, the total change in the number of bushels he has for sale after 7 days = 116.2
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HELP ! (Order of Operations with Radicals MC) Evaluate quantity the square root of 16 times 3 squared minus the cube root of negative 27 end quantity divided by 2 squared.
Help me asap this due in like a hour
Answer:
A: 2
B: 5
C: 4
D: 3
E: 1
Step-by-step explanation:
Looks right to me :)
The cost, c, for catering a luncheon using Right On Catering is c=120+12m+10v where m is the number of meat lunches and v the number of vegetarian lunches being served at the luncheon.
a.) Solve the equation for v.
b.) If the cost for the luncheon was $558 and 24 attendees ordered the meat lunches, how many vegetarian lunches were served?
Answer:
if the cost for the luncheon was $558
and 24 attendees ordered the meat lunches , how many vegetarian lunches were
Step-by-step explanation:
Answer:
Step-by-step explanation:
The sum of two consecutive integers is 187. Find the integers.
what is the answer to this problem?
10
_
8
Step-by-step explanation:
corect me if i wrong
Solve for x. please show work for answer on paper
3x – 8 – 4x = -13
A) 3 The weapon was not an algebra book.
B) -3 The weapon was not a promethean pen.
C) 5 The weapon was not a calculator.
D) -5 The weapon was not a protractor.
E) 5/7 The weapon was not cafeteria food.
Answer:
c) 5
Step-by-step explanation:
Solving for the value of x,
→ 3x - 8 - 4x = -13
→ 3x - 4x = -13 + 8
→ -x = -5
→ [ x = 5 ]
Thus, the value of x is 5.
Answer:
5
Step-by-step explanation:
Use PEMDAS
First you should do is to combine like terms
[tex] - x - 8 = - 13[/tex]
Haveing combined ike terms you need to add 8 to both sides (Like terms are terms that have the same variable like,x)
[tex] - x = - 5[/tex]
Then divide by a negative 1
(this is to get rid of negative x)
[tex]x = 5[/tex]
Hope this helps!
Feel free to ask questions
Tom and ben both get paid the same amount for every hour they work. tom worked 5 hours and ben worked 6 hours. together, they received r1 430. how much money did each receive?
Tom and Ben received 650 and 780 respectively.
Let the amount paid to each for every hour they work be x. Now, forming the equation as per the given information in question.
5x + 6x = 1430
Performing addition to find the value of x.
11x = 1430
Shifting 11 to Right Hand Side of the equation
x = 1430 ÷ 11
Performing division to find the value of x
x = 130
Now finding the amount received by Tom and Ben based on the number of hours they worked.
Amount received by Tom = 5x
Amount received by Tom = 5 × 130
Amount received by Tom = 650
Amount received by Ben = 6x
Amount received by Ben = 6 × 130
Amount received by Ben = 780
Therefore, the amount received by Tom and Ben are 650 and 780 respectively.
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Alexander said: "All primes are odd,
except the number 2. Therefore, all odd numbers are prime numbers.
prime." Do you agree with Alexander? Explain your answer.
No
Step-by-step explanation:
All numbers that are prime are odd and If the number is divisible by 2 it would be a composite number
Please help urgent!
Ex 3: Quadrilateral ABCD is a parallelogram.
a) m/BAC = 54°,
find m/DCA =
D
D
A
c) m/DCB = 142° & m/DCA =
37⁰,
find m/BAC=
D
A
E
A
E
7
C
e) AE = 14 cm & DE = 18 cm,
find EB =
E
B
?
C
B
B
find m/DAB =
D
D
d) m/ABC = 73° &
m/DBA = 31°,
find m/DBC =
b) m≤ADC = 78°,
D
A
A
A
E
O
E
f) EC = 10 cm & EB = 15 cm,
find AC =
E
C
B
OB
C
B
Answer:
36 = 69
Step-by-step explanation:
45
Solve the equation. 2(5 – 7) = 1
Answer:
False
Step-by-step explanation:
Distribute, do the math, and evaluate the resulting equality/statement to see if it is true
10 - 14 = 1
-4 = 1
That is not true so the answer is false
Fill in the gap to factorise -16z - 12 = −4(-
Answer:
- 4(4z + 3)
Step-by-step explanation:
- 16z - 12 ← factor out - 4 from each term
= - 4(4z + 3)
Pls pls help whoever gets it right gets a crown
Answer: -104y^2 + 52y
Step-by-step explanation:
-13y(8y-4)=
-13y*8y - 4(-13y)= ==> distribution property
-13*8*y*y - (-52y)=-104y^2 + 52y
30 points
how do i solve 4x -1
Answer: QV=31 units ==> 3rd option
Step-by-step explanation:
SV=QV ==> Congruent segments are equal
4x-1=QV
TQ=TS ==> Congruent segments are equal
26=3x+2
26-2=3x+2-2
3x=24
x=8
4x-1=QV
4(8)-1=QV
32-1=QV
QV=31 units ==> 3rd option
A square technology chip has an area of 81 centimeters. How long is each side of the chip?
The length of each side of the chip is ]]]blank]]]
enter your response here cm.
(Simplify your answer.)
The length of each side of the chip is 9 centimeters.
What is the length of each side of the chip?A square is an object that has four sides and four equal sides. All the four sides of a square are of equal length. A square has two diagonal that bisect each other at 90°.
The area of a square = length²
Given the area of a square, the length can be determined by calculating the square root of the area of the square. The square root of a number divides a number into two equal halves.
Length = √area
√81 = 9cm
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What scale factor would you use to create the copy on the right?
- - - - - - - - - - - - - - - - - - - - - - - -
Work below. Enjoy!
- - - - - - - - - - - - - - - - - - - - - - - -
A simple way to determine the scale factor is to measure a segment's size in units and compare it to the original.
Segment XW = 6 units
Segment EF = 2 units
Now, simply divide the larger (6) by the smaller (2) and you get your answer (3).
- - - - - - - - - - - - - - - - - - - - - - - -
Good luck! :)
(Consider leaving a Brainliest if this helped!)
~pinetreee
솓ㄱㄷ 샤 냐 :)
THERE...........
Answer:
60 percent
I think it is 60 but you might need a more certifyd answer
==================================================
Explanation:
A is 40% of B
This translates to the equation A = 0.40B or A = 0.4B
This is because 40% converts to 0.40 in decimal form
Let's divide both sides by 0.4 to isolate B
A = 0.4B
A/0.4 = B
B = (1/0.4)A
B = 2.5A
This shows that B is 250% of A
------------
Another approach:
40% = 40/100 = 2/5
"A is 40% of B" is the same as "A is 2/5 of B
So,
A = (2/5)*B
5A = 2B
2B = 5A
B = 5A/2
B = (5/2)A
B = 2.5A
which is another way to show that B is 250% of A
pls help me
Which expression is equivalent to -5 + 6
A:-5+6
B:5+6
C:5-6
D:6-5
Answer:
-5+6 = 1
6-5 = 1
therefore, the answer is D.
Answer:
D
Step-by-step explanation:
-5+6=+1
and 6-5=+1
since both are equal to 1
D is the answer
Kiara has $250 in her bank account. Each week she deposits $80 and withdraws $35. Gael has $310 in his account. Each week he deposits $95 and withdraws
$20. Write and solve an equation to determine the week w when Gael and Kiara have the same amounts of money in their account
The equation to determine the week w when Gael and Kiara have the same amounts of money in their account is 45w + 250 = 75w + 310
What is an equation?An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.
Let w represent the number of weeks.
For Kiara:
Money in account = (80 - 35)w + 250 = 45w + 250
For Gael:
Money in account = (95 - 20)w + 310 = 75w + 310
For both to have same amount of money:
45w + 250 = 75w + 310
The equation to determine the week w when Gael and Kiara have the same amounts of money in their account is 45w + 250 = 75w + 310
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Assume that Tom's Tree and Landscape Service charges $ 175 for a consultation fee plus $55 per hour for labor and that Lawn Perfect Landscape Service charges $325 for a consultation fee plus $25 per hour for labor.
a) Write a system of equations to represent the cost of the two landscaping services.
b) Graph both equations for 0 to 10 hours on the same axes.
c) Use the graph to estimate the number of hours of landscaping that must be used for both services to have the same cost.
Using linear functions, we have that:
a) The system is composed by these following equations: 175 + 55x, 325 + 25x.
b) The graph is given at the end of the answer.
c) From the point of intersection on the graph, both services will have the same cost of $450 for 5 hours of work.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For each function, we have that:
The consultation fee is the intercept.The hourly fee is the slope.Hence the linear equations that compose the system are given by:
175 + 55x, 325 + 25x.
The graph is given at the end of the answer, and from it, the intersection point is at (5,450), meaning that both services will have the same cost of $450 for 5 hours of work.
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Which mathematical term cannot be precisely defined? line segment point circle ray
I need help with these questions
Answer:
17. (2/5)
19. (-7/3)
21. (2/3)
Step-by-step explanation:
17.
5 5 1
- -------n + ------n = - ------
2 4 2
5 (2) 5 1 (2)
- -------n + ------n = - ------
2 (2) 4 2 (2)
10 5 2
- -------n + ------n = - ------
4 4 4
10 5 2
(- -------n + ------n = - ------) (4)
4 4 4
-10n + 5n = -2
-5n = -2
÷ -5 ÷-5
n = (2/5)
----------------------------------------------------------------------------------------------------------
19.
3 15 21
-------n - -------n = -------
2 4 4
3 (2) 15 21
-------n - -------n = -------
2 (2) 4 4
6 15 21
(-------n - -------n = -------) (4)
4 4 4
6n - 15n = 21
-9n = 21
÷-9 ÷-9
n = (-7/3)
----------------------------------------------------------------------------------------------------------
21.
1 5
- -------n - n = - -------
4 6
1 (3) 5 (2)
- -------n - n = - -------
4 (3) 6 (2)
3 10
- -------n - n = - -------
12 12
3 10
(- -------n - n = - -------) (12)
12 12
-3n - 12n = -10
--15n = -10
÷-15 ÷-15
n = (2/3)
----------------------------------------------------------------------------------------------------------
I hope this helps!
HELP URGENT!! EVERYTHING INCLUDED IN PHOTO!!
Answer:
Part A is 63-7.5
Step-by-step explanation:
Independent Practice For each pair of expressions below, without substituting in specific values, determine which of the expressions in the given pairs is larger. Explain your reasoning in a sentence or two.
In the first pair of numbers 15/x² + 6 is larger and in the second pair of numbers (s² + 2)/(s² + 1) is larger
What is Expression in Mathematics?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is two pairs of expressions. From the image given , we can write them as -
Pair 1 → f(x) = 15/x² + 6 and h(x) = 15/x² + 7
Pair 2 → f(s) = (s² + 2)/(s² + 1) and h(s) = (s² + 4)/(s² + 3)
We can compare which expression is larger in both the pairs without substituting any specific value as follows -
Pair 1 → f(x) = 15/x² + 6 and h(x) = 15/x² + 7.
The numerator is same in both the functions.
Now, for any value of x ∈ R → x² + 6 < x² +7 by 1. Therefore, f(x) > h(x)
Pair 2 → f(s) = (s² + 2)/(s² + 1) and h(s) = (s² + 4)/(s² + 3)
f(s) = (s² + 2)/(s² + 1) = [(s² + 1) + 1]/(s² + 1) = 1 + 1/(s² + 1)
h(s) = (s² + 4)/(s² + 3) = [(s² + 3) + 1]/(s² + 3) = 1 + 1/(s² + 3)
So, we can write that -
f(s) = 1 + 1/(s² + 1)
h(s) = 1 + 1/(s² + 3)
Now for any value of s → (s² + 1) < (s² + 3) by 2. So → 1/(s² + 1) > 1/(s² + 3). Therefore → 1 + 1/(s² + 1) > 1 + 1/(s² + 3). Finally, we can write -
(s² + 2)/(s² + 1) > (s² + 4)/(s² + 3)
Therefore, in the first pair of numbers 15/x² + 6 is larger and in the second pair of numbers (s² + 2)/(s² + 1) is larger.
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