a) Sample mean of set is 36.375.
b) Standard deviation of sample is 6.66208.
Define mean and standard deviation.The average degree of variability in your dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. In general, values with a large standard deviation are spread out from the mean, and those with a low standard deviation are grouped together near to the mean.
Given,
a) Mean
Total number of values = 16
= Sum/Total number of values
= 34 +45+ 27 +33 +38+ 41+ 45 +29 +30+ 39 +34 +40 +28 +33 +36+ 50/16
= 582/16
= 36.375
Sample mean of set is 36.375.
b) Sample standard deviation
S² = ∈ (x i - x)²/N-1
S² = 666.75/16-1
S² = 44.383333
S = √44.38333
S = 6.66208
Standard deviation of sample is 6.66208.
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Amy’s restaurant has budgeted at most $60 to spend this month on gourmet coffee. All international blends cost
$8.50 per package and all house blends cost $6.00 per package. She would like to purchase some international
blends and at least 3 packages of the house blends. Write a system of linear inequalities that describes this
situation. Graph the system. Give a possible solution and describe what it means
Answer:
8.50x + 6.00y < 60 and y > 3.
Please consider the complete question.
Amy's restaurant has a budget of at most $60 to spend this month on gourmet coffee. All international blends cost $8.50 per package and all house blends cost $6.00 per package. She would like to purchase some global combinations and at least 3 boxes of the house blends. Write a system of linear inequalities that describes this situation.
Let x represent the number of international blends and y represent the number of house blends.
The cost of x international blends would be and the cost of y house blends would be.
Since Amy's restaurant has a budget of at most $60 to spend this month on gourmet coffee, so the cost of x international blends and y house blends should be less than or equal to 60.
We can represent this information in an inequality as:
Since Amelia wants to purchase at least 3 packages of the house blends, so y should be greater than or equal to 3. We can represent this information in an inequality as:
Therefore, our required system of inequalities would be 8.50x + 6.00y < 60 and y > 3.
Step-by-step explanation:
Daniela needs to rent a car while on vacation. The rental company charges $19.95, plus 18 cents for each mile driven. If Daniela only has $50 to spend on the car rental, what is the maximum number of miles she can drive?
Daniela can drive a maximum of
going over $50. Round your answer to the nearest mile.
miles without the cost of the rental
Answer:
167 miles without the cost of the rental
Step-by-step explanation:
Daniela needs to rent a car while on vacation. The rental company charges $19.95, plus 18 cents for each mile driven. If Daniela only has $50 to spend on the car rental, what is the maximum number of miles she can drive? Round your answer to the nearest mile.
equation: where m = miles driven
50 = 0.18m + 19.95
subtract 19.95 from both sides:
50 - 19.95= 0.18m + 19.95 - 19.95
30.05 = 0.18m
divide both sides by 0.18:
30.05/0.18 = 0.18m/0.18
m = 166.9444
rounded: 167 miles without the cost of the rental
Answer:
167 :)
Step-by-step explanation:
it's math :)
A bad contains 7 red marbels and 4 blue marbles
A marble is taken from the bag and replaced
another marble is taken from the bag
Work out the probability that the two marbles are the same colour
Give your answer as a fraction
Answer:
I think its 7/3 or 6/4
Step-by-step explanation:
Answer:
Step-by-step explanation:
(a) Because there are 7 red and 4 blue marbles, there are 7+4=11 marbles in the bag.
So the ratio of all marbles to blue marbles is 11 to 4.
We write this as follows. 11:4
(b)There are 7 red marbles and 4 blue marbles in the bag.
So the ratio of red marbles to blue marbles is 7 to 4.
We write this as follows. 7:4
18^7 * 20^7 divided by 25^3 * 2^21 *27^4
Answer:
[tex]=45[/tex]
Step-by-step explanation:
1 ) Simplify
[tex]\frac{(18^7)(20^7)}{(25^3)(2^2^1)(27^4)}[/tex]
[tex]= \frac{612220032(20^7)}{(25^3)(2^2^1)(27^4)}[/tex]
[tex]= \frac{(612220032)(1280000000)}{(25^3)(2^2^1)(27^4)}[/tex]
[tex]= \frac{783641640960000000}{(25^3)(2^2^1)(27^4)}[/tex]
[tex]= \frac{783641640960000000}{15625(2^2^1)(27^4)}[/tex]
[tex]= \frac{783641640960000000}{(15625)(2097152)(27^4)}[/tex]
[tex]= \frac{783641640960000000}{32768000000(27^4)}[/tex]
[tex]= \frac{783641640960000000}{(32768000000)(531441)}[/tex]
[tex]= \frac{783641640960000000}{17414258688000000}[/tex]
[tex]=45[/tex]
Hope this helps! :)
Translate the following equation into a verbal sentence x/4 - y = -2(x/y)
The given equation x/4 - y = -2(x/y) can be expressed in a verbal sentence as the difference between the fourth fraction of x and y is equal to minus of twice the fraction of x and y.
How to express the mathematical equation in the form of a verbal sentence?
To express the mathematical equation in the form of a verbal sentence, we have to express the operations by using sentences.
Let's take an example,
x + y = 4.
Then the verbal form will be the sum of two numbers is 4.
Hence, the given expression can be expressed as the difference between the fourth fraction of x and y is equal to minus of twice the fraction of x and y.
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I need help like asap !!!
only numbers and decimal points
Answer:
34 inches
Step-by-step explanation:
[tex]c = \sqrt{ {16}^{2} + {30}^{2} } [/tex]
[tex]c = \sqrt{256 + 900} [/tex]
[tex]c = \sqrt{1156} = 34[/tex]
Answer:
34 inches...................
Henry Bonnacio deposited 1,000 in a new savings account at First National Bank. He made no other deposits or withdrawls. After 6 months the interset was computed at an annual rate of 6 1/2%. How much simple interst did his money earn.
Please helppp!
1 :What is the solution to the equation?
−4=x9
2 :Solve for t.
−32=4t
Responses
t=−8
t equals negative 8
A:T = -8
B:T = - 1/8
C:T= 28
D:T=36
3 : What is the solution to the equation?
x−18=−72
4 ;What is the solution to the equation?
−18=x−15
Enter your answer in the box.
5 :What is the solution to the equation?
−24x=−4
Enter your answer as a simplified
The value of the variables in the equation are as follows:
1. x = -4 / 9
2. t = -8
3. x = -54
4. x = -3
5. x = 1 / 6
How to solve an equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Let's find the solution of the equations. The solution of the equation is the value of the variable x. A variable is a number represented by a letter in an equation.
Therefore,
1.
-4 = 9x
divide both sides of the equation by 9
x = - 4 / 9
2.
−32=4t
divide both sides of the equation by 4
t = - 32 / 4
t = - 8
3.
x − 18 = −72
add 18 to both sides of the equation
x - 18 + 18 = -72 + 18
x = -54
4.
−18 = x − 15
add 15 to both sides of the equation
-18 + 15 = x - 15 + 15
-3 = x
x = -3
5.
−24x = −4
divide both sides of the equation by - 24
x = - 4 / -24
x = 1 / 6
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I need help please because I am failing in math
Answer:
what do you need help with?
Answer:
Step-by-step explanation:
You need a picture of the item.
The rate of change of f(x)=2(2)x is ____________________ the rate of change of the function in the graph:
The rate of change of the exponential function f(x) = 2(2)ˣ is 2
What is an equation?An equation shows the relationship between two or more numbers and variables.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the rate of change.
Given the function:
f(x) = 2(2)ˣ
Hence rate of change = 2
The rate of change is 2
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If p * q = 3p + 2q – 5, then 3 * 2 =
Work Shown:
p * q = 3p + 2q - 5
3 * 2 = 3(3) + 2(2) - 5
3 * 2 = 9 + 4 - 5
3 * 2 = 13 - 5
3 * 2 = 8
A dolphin was swimming at 20 feet below sea level. Then it dove to 45 feet below its original position. Write an expression that represents the change in depth of the dolphin's dive.
The expression that represents the change in depth is |-45 + 20|
How to determine the change in depth expression?From the question, the endpoints are given as
Initial point = 20 feet below the sea level
Final point = 45 feet below the sea level
Rewrite the endpoints properly
This is done as follows
Initial point = -20
Final point = -45
The distance expression between the endpoints is then calculated as
Distance = |Final point - Initial point|
Substitute the known values in the above equation
So, we have the following equation
Distance = |-45 + 20|
Hence, the distance expression is |-45 + 20|
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Container A has 600 mL of water and is being filled at a rate of 12 mL per minute. Container B has 1500 mL of water and is being drained at 12 mL per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Answer:
It will take 37.5 minutes for both containers to reach the same amount of water which is 1050 mL
Step-by-step explanation:
1500 - (12 × 37.5) = 1050
600 + (12 × 37.5) = 1050
Use either long division or synthetic division to solve:
(2i^4 +-6i³+-25i² +31i+-30)/(i +-5)
Answer:
[tex]\textsf{Quotient}: \quad 2i^3+4i^2-5i+6[/tex]
[tex]\textsf{Simplified Quotient}: \quad 2-7i[/tex]
Step-by-step explanation:
Long division method
Divide the first term of the dividend by the first term of the divisor, and put that in the answer.Multiply the divisor by that answer, put that below the dividend.Subtract to create a new dividend.Repeat.Given rational expression:
[tex]\dfrac{2i^4-6i^3-25i^2 +31i-30}{i -5}[/tex]
Solve using long division:
[tex]\large \begin{array}{r}2i^3+4i^2-5i+6\phantom{)}\\i-5{\overline{\smash{\big)}\,2i^4-6i^3-25i^2 +31i-30\phantom{)}}}\\{-~\phantom{(}\underline{(2i^4-10i^3)\phantom{-b00000000000.)}}\\4i^3-25i^2+31i-30\phantom{)}\\-~\phantom{()}\underline{(4i^3-20i^2)\phantom{))))))))))))}}\\-5i^2+31i-30\phantom{)}\\-~\phantom{()}\underline{(-5i^2+25i)\phantom{........}}\\6i-30\phantom{)}\\-~\phantom{()}\underline{(6i-30)\phantom{}}\\0\phantom{)}\end{array}[/tex]
Therefore, the quotient is:
[tex]2i^3+4i^2-5i+6[/tex]
Imaginary number rule
[tex]i^2=-1[/tex]
Simplify the quotient:
[tex]\implies 2i^3+4i^2-5i+6[/tex]
[tex]\implies 2i^3+4(-1)-5i+6[/tex]
[tex]\implies 2i^3-4-5i+6[/tex]
[tex]\implies 2i^3-5i-4+6[/tex]
[tex]\implies i(2i^2-5)+2[/tex]
[tex]\implies i(2(-1)-5)+2[/tex]
[tex]\implies-7i+2[/tex]
[tex]\implies 2-7i[/tex]
A palindrome is a word or number that is the same when read forwards or backwards. For example, DAD is a palindrome, and so is
RACECAR. 484 is a palindrome number, and so is 9229.
What is the sum of a three digit palindrome number that ends in 71 and a four digit palindrome number that ends in 83?
Answer:
4054
Explanation:
171 is the three-digit palindrome that ends with 71
3883 is the four-digit palindrome that ends with 83
171 + 3883 = 4054
engineers must consider the diameters of heads when designing helmets. the company researchers have determined that the population of potential clientele have head diameters that are normally distributed with a mean of 6.4-in and a standard deviation of 0.9-in. due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 1.4% or largest 1.4%. what is the minimum head diameter that will fit the clientele? min
The largest head diameter that can accommodate the clientele is 8.5743
Mean, u = 6.4
Standard deviation = 0.9
We must utilize the inverse of the common normal table to obtain our values.
the smallest head width possible.
P(Z < z) = 1.4%
P(Z < z) = 0.014
P(Z < -2.0749) = 0.014
z = -2.0749
Using the z-score calculation,
(x - μ) ÷ σ = [tex]Z_{0.019}[/tex]
Let x be the heads' breath.
Making x the focus of the equation,
x = z × σ + μ
We already have:
z = -2.0749
u = 6.5
s.d = 1
Replacing numbers,
x = (-2.0749 × 1) + 6.5
x = 4.4251
The clientele requires a minimum head breadth of 4.4251.
The largest head width that can be accommodated.
P(Z > z) = 1.4%
1 - P(Z < z) = 0.014
P(Z < z) = 1 - 0.014 = 0.981
P(Z < 2.0749) = 0.981
Using the z-score calculation,
(x - μ) ÷ σ = [tex]Z_{0.019}[/tex]
Let x be the heads' breath.
Making x the focus of the equation,
x = z × σ + μ
z = 2.0749
u = 6.5
s.d = 1
Substituting figures,
x = (2.0749 × 1) + 6.5
x = 4.4251
x = 8.5743
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Need Help With Explaining and ASAP please! And check if I’m correct!
Answer:
yhj
Step-by-step explanation:
all in the text bag with you high bag GM DJ tee SB hy DJ DJ TV DJ DJ DJ DJ CB jus DJ tty 464+7557+56(6)=7
Y = 5x -12 make x subject of formula
Answer:
(y+12)/5=x
Step-by-step explanation:
y=5x-12
get x by itself
y+12=5x
divide both sides by 5
(y+12)/5=x
Sophia spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -2.1°F. Between 9am and noon, the temperature increased by 10.8°F. Between noon and 3pm, the temperature decreased by 13°F. Between 3pm and 6pm, the temperature dropped 18.4°F. What was the temperature at 6pm?
PLEASE HURRY I NEED IT FAST
Using mathematical operations, we know that temperature after 6 p.m. will be -22.7°F.
What exactly are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).So, the temperature after 6 p.m. will be:
The temperature at different times:
At 9 a.m. = -2.1°FBetween 9 - 12 = +10.8°FBetween 12 - 3 = -13°FBetween 3 - 6 p.m. = -18.4Now, calculate to get the temperature after 6 p.m. as follows:
= -2.1 + 10.8 - 13 - 18.4 = -22.7°FTherefore, using mathematical operations, we know that the temperature after 6 p.m. will be -22.7°F.
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2. Identify the proportional relationship.
7x-2=y y + 1 = 3x y = 5x y=2x +4
In class, everyone took a handful of m&ms, so people had a mean of
37 with a standard deviation of 7. Ms G hands everyone 10 more
m&ms. What is the new mean?
Isabel and Khalil buy peaches and apricots. At the fruit stand, peaches cost $0.85 each, and apricots cost $0.55 each. Tax is included in the cost of each fruit. The friends have $5 to spend. Which is a possible combination of the number of peaches and apricots they can get for $5? Responses 1 peach, 8 apricots 1 peach, 8 apricots 2 peaches, 5 apricots 2 peaches, 5 apricots 3 peaches, 7 apricots 3 peaches, 7 apricots 4 peaches, 3 apricots 4 peaches, 3 apricots
The possible combination of the number of peaches and apricots they can get for $5 is 2 peaches and 5 apricots.
What is the possible combination?The equation that represents the total cost of peaches and apricots is:
Total cost = (number of peaches x cost of one peach) + (number of apricots x number of apricots)
$5 = ($0.85 x p) + ($0.55 x a)
Total cost of buying 1 peach and 8 apricots:
($0.85 x 1) + ($0.55 x 8) = $5.25
Total cost of buying 2 peaches and 5 apricots:
($0.85 x 2) + ($0.55 x 5) = $4.45
Total cost of buying 3 peaches and 7 apricots:
($0.85 x 3) + ($0.55 x 7) = $6.40
Total cost of buying 4 peaches and 3 apricots:
($0.85 x 4) + ($0.55 x 3) = $5.05
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Circle 10cm find the diameter of the circle
Answer:
Diameter = 3.1831 cm (aprox)
Step-by-step explanation:
Diameter = circle / π
π ≈ 3.1414
Then:
Diameter = 10 / 3.1418
Diameter = 3.1831 cm
the normal model n(58, 21) describes the distribution of weights of chicken eggs in grams. suppose that the weight of a randomly selected chicken egg has a z-score of 1.78. what is the weight of this egg in grams? round to the nearest hundredth of a gram.
The weight of the eggs in grams 95.38 grams.
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
X ~ N(58,21)
where µ = 58 and σ = 21
The z score for this case is given by this formula:
z = x - µ/σ
We know that the value of z = 1.78 and we want to estimate the value of X. If we solve for X from the z formula we got:
X = µ+1.78σ
= 58 + 1.78×21
= 95.38
So, the corresponding weight for a z score of 1.78 is 95.38 grams.
Hence we get the required answer.
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PLEASE HELP ASAP express
Answer: 5+3*3(3)-2= 30
Step-by-step explanation: Replacing x with 2 and using PEMDAS
Ramundo is shopping for a new pair of rollerblades. Roller World sells a pair of rollerblades for $94 regular price. Currently, the rollerblades are on sale for 15% off. Outdoor Adventures sells the same pair of rollerblades for $81.50 with no discount. The sales tax rate in Ramundo's city is 6%.
Part A
To get the better deal, Ramundo should buy the rollerblades from , 1 of 2.
Select Choice
.
Part B
In doing so, he will save , 2 of 2.
Select Choice
(after tax) over the other store.
Ramundo will get a better deal at Roller worlds.
This is a question of percentages.
Given that:-
Regular price of rollerblades at roller world = $ 94
Discount at rollerworld = 15 %
Price of rollerblades at Outdoor adventures = $ 81.50
Sales tax = 6 %
Price of rollerblades at roller world after discount = 94 - (15/100)*94 = 94 - 14.1 = $79.9
Price of rollerblades at roller world after sales tax = 79.9 + (6/100)*79.9 = 79.9 + 4.794 = $ 84.694
Price of rollerblades at outdoor adventures = $81.50
Price of rollerblades at roller world after sales tax = 81.50 + (6/100)*81.50 = 81.50 + 4.89 = $ 87.39
As,
$ 84.694 < $ 87.39
Ramundo will get a better deal at Roller worlds.
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What is the amount of m
Answer:
N=138
Step-by-step explanation:
(4x+6) + N = 180
In order to complete this problem we need to solve for x. 4x+6=7x-21
Subtract on both sides
Subtract again
Divide
x=9
Plug it in now so 4 times 9 plus 6. 36, plus 6 = 42.
plug it in to the equation 42+N=180
-42 -42
138 = N
(b) Expand and simplify.
(2x - 5) (x - 3)
help me pls
[tex] = 2x(x - 3) - 5(x - 3) \\ = 2 {x}^{2} - 6x - 5x + 15 \\ = 2 {x}^{2} - 11x + 15 [/tex]
ATTACHED IS THE SOLUTION
At a certain time, Janice notices that her digital watch reads a minutes after two o'clock. Fifteen minutes later, it reads b minutes after three o'clock. She is amused to note that a is six times b. What time was it when she looked at her watch for the second time?
Answer:
2 : 45
Step-by-step explanation:
What are the roots of the equation x 2 + 16 x + 80 = 0 x 2 +16x+80=0 in simplest a + b i a+bi form?
The quadratic equation x² + 16 · x + 80 has two roots: x₁ = - 1 / 10 + i (4 / 5), x₂ = - 1 / 10 - i (4 / 5).
How to determine the roots of a quadratic equation
In this question we find a quadratic equation of the form a · x² + b · x + c = 0, whose roots can be found by using the quadratic formula:
x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)
Where b² - 4 · a · c is the discriminant of the quadratic formula, which offers three cases of solutions:
b² - 4 · a · c > 0: Two different real roots. b² - 4 · a · c = 0: Two equal real roots. b² - 4 · a · c < 0: Two conjugate complex roots.If we know that a = 1, b = 16 and c = 80, then the roots of the quadratic equation are, respectively:
x = - 16 / 160 ± (1 / 160) · √(16² - 4 · 1 · 80)
x = - 1 / 10 ± (1 / 10) · √(- 64)
x = - 1 / 10 ± i (4 / 5)
The roots are - 1 / 10 + i (4 / 5) and - 1 / 10 - i (4 / 5).
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