Answer:
A customer will get 1 gallon for $3.50.
A customer will pay $ 21 for 6 gallons.
A customer will get 4 gallons for $14.00.
A customer will get 2 gallons for $7.00.
Step-by-step explanation:
This is solved using the unitary method .
Four gallons cost $ 14
1 gallon costs $ 14/4= $ 3.5
6 gallons cost = $ $ 14/4 *6= $ 21
2 gallons cost = $ 14/4 *2= $14/2= $ 7
A customer will get 1 gallon for $3.50.
A customer will pay $ 21 for 6 gallons.
A customer will get 4 gallons for $14.00.
A customer will get 2 gallons for $7.00.
This can be found out by using the direct ratio as well.
Gallons Cost
4 $14
1 x
Using cross product
x*4= $ 14*1
x= $ 14/4 = $3.5
The same can be applied to find the rest and we get the same answers.
A well-mixed cookie dough will produce cookies with a mean of 8 chocolate chips apiece. What is the probability of getting a cookie with no more than 3 chips
Answer:
The probability of getting a cookie with no more than 3 chips is 0.0424.
Step-by-step explanation:
Let X number of chocolate chips apiece of cookie.
The mean number of chocolate chips apiece is λ = 8.
The random variable X follows a Poisson distribution with parameter λ = 8.
Compute the probability of getting a cookie with no more than 3 chips as follows:
[tex]P(X\leq 3)=\sum\limits^{3}_{x=0}{\frac{e^{-8}(8)^{x}}{x!}}[/tex]
[tex]=0.00034+0.00268+0.01073+0.02863\\=0.04238\\\approx 0.0424[/tex]
Thus, the probability of getting a cookie with no more than 3 chips is 0.0424.
A square-based, box-shaped shipping crate is designed to have a volume of 16 cubic ft. The material used to make the base costs twice as much (per square foot) as the material in the sides, and the material used to make the top costs half as much (per square foot) as the material in the sides. What are the dimensions of the crate that minimize the cost of materials
Answer:
Step-by-step explanation:
dimension
base=x, height =y, as they both are length so x, y >0
Volume of the crate= [tex]x^2y[/tex] = [tex]16ft^3[/tex]
cost
base=b unit money /[tex]ft^2[/tex]
side material = b/2 unit money /[tex]ft^2[/tex]
Top view= b/4 unit money /[tex]ft^2[/tex]
Total Cost=[tex]bx^2 + \frac{b}{2} *4xy + \frac{b}{4} *x^2[/tex] = [tex]2b( \frac{5}{8} *x^2 + xy)[/tex]
function to be minimized = [tex]\frac{5}{8}*x^2 + xy\\[/tex] , [tex]x^2y =16[/tex]
put [tex]y=16/x^2[/tex]
f(x) = [tex]\frac{5}{8}*x^2 + x*\frac{16}{x^2}[/tex]
upon differentiating this equation
f'(x)=0
[tex]\frac{5}{4}*x -16x^-2 = 0[/tex]
upon solving this we get [tex]x=4/\sqrt[3]{5}[/tex] [tex]y= \sqrt[3]{25}[/tex]
and further testing we get f"([tex]\frac{4}{\sqrt[3]{5} }[/tex]) >0 which proves that the point is local minimum.
Hence these are the dimensions of crate that minimizes the cost of material.
The dimensions that minimize the total cost of making the surface materials are [tex]2.3ft \text{ by } 2.3ft \text{ by }2.9ft[/tex]
[tex]T=\text{Total cost of materials}\\m_b=\text{unit cost of materials used to construct the base}\\m_t=\text{unit cost of materials used to construct the top}\\m_s=\text{unit cost of materials used to construct the sides}[/tex]
from the question, the crate has a square base and the volume is [tex]16ft^3[/tex]. So,
[tex]V=l^2h=16\\\implies h=\frac{16}{l^2}[/tex]
Also,
[tex]m_b=2m_s\\m_t=\frac{m_s}{2}[/tex]
Construct the formula for [tex]T[/tex],
[tex]T=l^2\times m_b + l^2 \times m_t+4lh\times m_s[/tex]
[tex]\text{where } l=\text{length of side of base/top}\\h=\text{height}[/tex]
Eliminating [tex]h, m_b, \text{ and }m_t[/tex], we have
[tex]T=m_s(\frac{5l^2}{2} + \frac{64}{l})[/tex]
differentiating wrt [tex]l[/tex] ([tex]m_s[/tex] is a constant), we have
[tex]\frac{dT}{dl}=m_s(5l-\frac{64}{l^2})[/tex]
The minimum total cost occurs when
[tex]m_s(5l-\frac{64}{l^2})=0[/tex]
or, when
[tex]l=\frac{4}{\sqrt[3]{5}} \approx 2.3[/tex]
(On carrying out the second derivative test, [tex]\frac{d^2T}{dl^2}>0[/tex] when [tex]l=\frac{4}{\sqrt[3]{5}}[/tex])
[tex]h=\frac{16}{l^2}=\sqrt[3]{5}^2\approx 2.9[/tex]
Therefore, the dimensions that minimize the total cost of making the surface materials are [tex]2.3ft \text{ by } 2.3ft \text{ by }2.9ft[/tex]
Another solved minimization problem can be found in the link: https://brainly.com/question/17116786
Buck is likely a proxy for whom in Jack London's life?
London's mother
London's father
London's favorite dog
London himself
Answer:
I think The answer is C. London's favorite dog
Answer: London himself
Step-by-step explanation: I just did the assignment and read the passage and It said buck was a proxy of London himself
1. Which of these statements describes a key distinction between an observational study and an experimental study?
A: Experimental studies are more representative of the larger population than observational studies.
B: Data is collected in experimental studies, but not in observational studies.
c: Observational studies try to answer a question, but experimental studies do not.
D: Experimental studies directly influence something to see its effect, but observational studies do not directly influence the subjects.
Answer: Experimental studies directly influence something to see its effect, but observational studies do not directly influence the subjects.
Step-by-step explanation:
The correct option is D.
In an experimental study, you perform an experiment. In an experiment are made with the objective of validating, refute, or support a given hypothesis, where you observe "what happens" when you modify a given set of parameters. Always in an experiment, we can define the independent and dependent variables, where the independent are the ones that we can modify at will, and the dependent ones are the ones that we observe to see how they react to the changes in the independent variables.
In observational studies, the idea is not changing anything in the object of study, so the scientist in this case are only observers or spectators.
28.98 = ___ x 10 to the what power?
Answer:
well if you do 2.898x10 you get 28.98.
Step-by-step explanation:
A decision maker is interested in estimating a population proportion. A sample of size n150 yields 115 successes. Based on these sample data, construct a 90% confidence interval estimate for the true population proportion. A. (0.714, 0.826) B. (0.717, 0.823) C. (0.750, 0.790) D. (0.737, 0.803)
A. (0.714, 0.826)
Step-by-step explanation:
Given that:
The sample size n = 150
The number of success(sample proportion) x = 115
The population proportion [tex]\hat p[/tex] = [tex]\dfrac{x}{n}[/tex]
The population proportion [tex]\hat p[/tex] = [tex]\dfrac{115}{150}[/tex]
The population proportion [tex]\hat p[/tex] = 0.767
At 90% confidence interval level;
[tex]Z_{\alpha /2} = Z_{0.05} = 1.645[/tex]
Thus, the confidence interval estimate for the true population proportion can be computed by using the formula:
[tex]=\hat p \ \pm \ z_{\alpha /2} \sqrt{\dfrac{\hat p(1- \hat p)}{n} }[/tex]
[tex]= 0.767 \ \pm 1.645 * \sqrt{\dfrac{0.767(1- 0.767)}{150} }[/tex]
[tex]= 0.767 \ \pm 1.645 * \sqrt{\dfrac{0.767(0.233)}{150} }[/tex]
[tex]= 0.767 \ \pm 1.645 * \sqrt{\dfrac{0.178711}{150} }[/tex]
[tex]= 0.767 \ \pm 1.645 * \sqrt{.0011914}[/tex]
[tex]= 0.767 \ \pm 1.645 * 0.03452[/tex]
[tex]= 0.767 \ \pm 0.0568[/tex]
= (0.767 - 0.0568, 0.767 + 0.0568)
= (0.7102 , 0.8238 )
Due to approximation; the confidence interval estimate for the true population proportion is [tex]\simeq[/tex] (0.714, 0.826)
AB = 4x + 6 and BC = 72 + 15. if AC = 120, find the length of segment AB.
Answer:
AB=33, x=6.75
Step-by-step explanation:
In order to solve this equation, draw a line with three points labeled A, B, and C. Then fill out what you know with the given information being AB=4x+6 and BC=72+15, then AC=120. then follow these steps:
Write the following equation: 4x+6+72+15=120Add like terms: 4x+93=120Subtract 93 from both sides, isolating the variable (x): 4x=27Divide both sides by 4 to get x=6.75Now that we know that x=6.75, follow these steps:
Plug in x to the equation: 4(6.75)+6 to find the length of AB, and the answer would be 33.I hope this helps!!!
12/7=5/2y What is y thanks
Answer:
y=24/35
Step-by-step explanation:
help please asap lol
Answer:
The measure of angle F is 78°.
A mechanic charges $55 for an engine check and $25 per hour foe his services. Which of the following is a linear model of his charges
Answer:
y=25x+55. $55 is a one-time fee while the $25 is per hour
Let X be a random variable with mean 6.1 and variance 2.4. Let Y be a random variable with mean 7.5 and variance 3.2. Find the variance of Z, Var(Z).
Answer:
Var(z)= 8.122 if Z= z1+z2
Step-by-step explanation:
IF x and Y are independent then Cov(x,y)= 0
Var(x+y) = Var X + Var y + 2cov(x,y)
= 2.4 + 3.2 +0 = 5.6
Z1= X - E (X)/ √Var (X) and Z2 = Y - E(Y)/ √Var Y
Var (z1+z2) = Var (z1) + Var(z2) + 2Cov (z1,z2)
Cov (z1,z2)= E(z1,z2) - E(z1) E(z2)
= E(z1,z2) [as E(z1) E(z2)= 0]
= E {[ X-E(X)] [Y-E(Y)]/ √Var(X) Var(y)}
= E{[ X- 6.1][Y- 7.5]/√2.4(3.2)}
= E {xy-7.5x -6.1y +45.75]/ 2.771}
={ 6.1(7.5) - 7.5(6.1) - 6.1(7.5) + 45.75]/ 2.771}
= 0/2.771
= 0
Var (z1+z2) = Var (z1) + Var(z2)
= {E (X)/ √Var (X)} +{ Y - E(Y)/ √Var Y}
= {6.1/√2.4 } + {7.5/√3.2}
= 3.93+ 4.19
=8.122
x:y=5 :3 and x+y=56 work out x-y
Answer:
The value of x - y is 14
Step-by-step explanation:
∵ x : y = 5 : 3
→ Write it in the form of the fraction
∴ [tex]\frac{x}{y}=\frac{5}{3}[/tex]
→ Multiply both sides by y
∴ [tex]\frac{x}{y}[/tex] × y = [tex]\frac{5}{3}[/tex] × y
∴ x = [tex]\frac{5}{3}[/tex] y ⇒ (1)
∵ x + y = 56 ⇒ (2)
→ Substitute x in (2) by (1)
∴ [tex]\frac{5}{3}[/tex] y + y = 56
→ Add the like terms
∵ [tex]\frac{8}{3}[/tex] y = 56
→ Divide both sides by [tex]\frac{8}{3}[/tex]
∴ y = 21
→ Substitute the value of y in (1) to find x
∵ x = [tex]\frac{5}{3}[/tex] (21)
∴ x = 35
→ Now find the value of x - y
∵ x - y = 35 - 21
∴ x - y = 14
∴ The value of x - y is 14
Hi guys im subtracting integers what is 17-12
Answer:
10
Step-by-step explanation:
I’m joking it actually 5
Answer:
5....?
Step-by-step explanation:
Which fration is equvalent to 12 1/12
Answer:12 2/24
If this helped please leave a brainliest it would really help out!
4. Calculate the probability that an officer is promoted given that the officer is a man. 5. Calculate the probability of a promotion given that the officer is a woman
Answer:
4. Probability of being promoted given the officer is a man = 0.3
5. Probability of a promotion given that the officer is a woman = 0.15
Note: The data table is found in the attachment below
Step-by-step explanation:
Probability = number of required outcomes/ number of possible outcomes
4. Probability of being promoted given the officer is a man
Probability of being promoted given the officer is a man = number of men promoted/total number of men
From the table, total number of men = 960
number of men promoted = 288
Probability of being promoted given the officer is a man = 288/960 = 0.3
5. Probability of a promotion given that the officer is a woman
Probability of a promotion given that the officer is a woman = number of women promoted/total number of women
From the table, total number of women = 240
number of women promoted = 36
Probability of a promotion given that the officer is a woman = 36/240 = 0.15
What division problem does the model represent?
Divided by one-third
The quotient is .
Answer:
the real answer is
5/3
divided by 1/3
and the quotient is
5
this is the real answer
Step-by-step explanation:
From the diagram attached, the divison operation represented by the model is [tex]\frac{7}{4} \div \frac{1}{2} = 3 \frac{1}{2}[/tex]
Each partition = 0.25 = 1/4 Number of shaded partitions = 7Number of partitions per rectangle = 4The Fraction of shaded partitions = 7(1/4) = 7/4
Half of each rectangle is circle = 1/2
Hence, the divison exemplified by the model is :
Fraction of shaded partition ÷ Circled portion
[tex]\frac{7}{4} \div \frac{1}{2}[/tex]
Take the reciprocal of 1/2 and change sign to multiplication :
[tex]\frac{7}{4} \times \frac{2}{1} = 3 \frac{1}{2}[/tex]
Therefore, the division problem represented by the model is [tex]\frac{7}{4} \div \frac{1}{2} = 3 \frac{1}{2}[/tex]
Learn more :https://brainly.com/question/18109354
3. Using exponents, what is the simplified form of (–2x2 y3)3???
Answer:
[tex]-8x^{6}y^{9}[/tex]
Step-by-step explanation:
[tex] (-2x^2y^3)^3 = [/tex]
[tex] = (-2)^3(x^2)^3(y^3)^3 [/tex]
[tex] = -8x^{2 \times 3}y^{3 \times 3} [/tex]
[tex] = -8x^{6}y^{9} [/tex]
10( x+1/2)=3x+5+7x
Please help
Answer:
All real numbers are solutions
Step-by-step explanation:
10(x + 1/2) = 3x + 5 + 7x
~Distribute left side
10x + 5 = 3x + 5 + 7x
~Combine like terms
10x + 5 = 10x + 5
~Subtract 5 to both sides
10x = 10x
~Divide 10 to both sides
x = x
~Subtract x to both sides
0 = 0
Best of Luck!
There is a rope it is divided into three piece it is divided into a ratio of 2 to 3 to 4 the biggest piece is 16 . What is the length of the original rope .
Answer:
I think the answer is 25.
Step-by-step explanation:
All you need to do is add up all the numbers
also aren't you in college!!!!‼️ASAP!!! BRAINLIEST!!‼️
PLS HELP!!! SHOW ALL WORK +STEPS!! Thx!
Answer:
y=-3/4+7
Step-by-step explanation:
slope formula is y2-y1 over x2-x1
4-7/4-0=
-3/4
and line intercepts at 7
A bag contains 42 cups of dog food. Your dog eats 2 1/3 cups of dog food each day. How many days does the bag of dog food last?
Answer:
18 days
Step-by-step explanation:
2 1/3 just 7/3. Next, divide 42 by 7/3 which is just 42/1 times 3/7 which gives you 18.
PLease help. will give brainliest to right answer
Answer:
the second bubble, [tex]\frac{1}{6^{2} }[/tex]
Step-by-step explanation:
[tex]6^{-2}[/tex] = [tex]\frac{1}{6^{2} }[/tex]
Answer:
1/6^2
the second one
Step-by-step explanation:
1. replace a with 6:
6^-2 6 to the power of negative two
2. solve;
when you have something to the power of a negative number, it gets smaller, so think: what is 6^2? (six to the power of two) That is 36. As a fraction, that would be 36/1. Since the 2 is negative, flip it to get 1/36.
1/6^2 and 1/36 are equal since 6^2 = 36
Hope this helps :)
What is f(g(x)) when f(x) = x ^ 2 + 5 , and g(x) = 10 - 5x ?
A function f (x) and g (x) then:
(f + g) (x) = x² - x + 6
Further explanation
Like the number operations we do in real numbers, operations such as addition, installation, division or multiplication can also be done on two functions.
Suppose a function f (x) and g (x) then:
(f + g) (x) = f (x) + g (x)
(f + g) (x) is a new function of the sum of f (x) and g (x)
Likewise with other function operations:
(f-g) (x) = f (x) - g (x)
(fg) (x) = f (x) x g (x)
(f / g) (x) = f (x) / g (x)
In addition to the above operations we can combine two functions using the function composition with the symbol o
(fog) (x) = f ((g (x))
Known on the question
f (x) = x² + 1
g (x) = 5 x
Summing the two functions f (x) and g (x):
(f + g) (x) = f (x) + g (x)
(f + g) (x) = x² + 1 + 5 - x
(f + g) (x) = x² - x + 6
A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $400 and the daily rate for each partner is $1000. The law firm assigned a total of 13 lawyers to the case and was able to charge the client $8800 per day for these lawyers' services. Write a system of equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case. Define the variables that you use to write the system.
Answer:
see below
Step-by-step explanation:
Variables:
Associate: a
Partner: p
Equations:
400a + 1000p = 8800
a + p = 13
Solve:
a + p = 13
a = 13 - p
400a + 1000p = 8800
400(13 - p) + 1000p = 8800
5200 - 400p + 1000p = 8800
5200 + 600p = 8800
5200 + 600p = 8800
600p = 3600
p = 6 partners
a = 13 - p
a = 13 - 6
a = 7 associates
The required number of associates is 7 and the number of partners is 6.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let the number of associated be x and the number of partners is y,
According to the question, x + y = 13
x = 13 - y - - - -- - - - - (1)
400x + 1000y = 8800 - - - - - - - - - -- (2)
From equation 1
400 (13 - y) + 1000y = 8800
4(13 - y) + 10y = 88
52 - 4y + 10y = 88
6y = 88 - 52
6y = 36
y = 6
Now, from equation 1
x = 13 - 6
x = 7
Thus, the required number of associates is 7 and the number of partners is 6.
Learn more about arithmetic here:
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Please help me 80 points and a branlist plz answer : (
Answer:
A. 2, 4
B. 4, 4
C. -1, -4
Step-by-step explanation:
Because in mathematics, a reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis or plane of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection.
So for A. just reflect the point over or "across the x-axis."
For B. just reflect the point over or "across the x-axis."
And for C. just reflect the point over or "across the y-axis."
Hope this helped!
Have a nice day!
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A. 2, 4
B. 4, 4
C. -1, -4
A perimeter of a rectangle is 200 yards. What are the dimensions of the rectangle if the length is 80 yards more than the width
which point represents -2 3/8 on the number line?
Answer:
answer wil be point c because as shown
How many is (+5) --(692)+1/3%
Answer:
730.3
Step-by-step explanation:
hope this helps.
Write a function rule for the problem
Answer:
er
Step-by-step explanation:
Answer:
What function?
Step-by-step explanation:
Can you provide me with the problem.
Johnathan is 5 years younger than his brother Paolo. The sum of the brothers ages is 47. How old is Johnathan
Step-by-step explanation:
let, the age of Jonathan be X and Paolo be X+5,
then,
x+x+5=45
2x=40
x=20
: Therefore the age of Jonathan is 20 and Paolo is 20+5=25.
If Johnathan is 5 years younger than his brother Paolo. The sum of the brothers ages is 47. Then Johnathan is 21 years old.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The sum of the brothers ages is 47.
Let the age of Paolo is x
Johnathan is 5 years younger than his brother Paolo
Johnathan age=x-5
As given, sum of the brothers ages is 47.
x+x-5=47
2x-5=47
2x=47+5
2x=52
Divide both sides by 2
x=26
So the age of Paolo is 26 and Jaohnathan age is 26-5=21 years.
Hence Johnathan is 21 years old.
To learn more on Equation:
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