The simplified form of the expression is 4x² - 3x + 2
Answer:
[tex]4x^{2} - 3x + 2[/tex]
Step-by-step explanation:
[tex](2x^{2} + x) - (-2x^{2} + 4x - 2)\\\\2x^{2} + x + 2x^{2} - 4x - 2\\\\\\4x^{2} -3x+2[/tex]
In an examination ,55%examines passed in english,60%In mathematics .if 40% examines passed in both subject.
1.By using Venn diagram
2.Find the percentage of students who failed in both the subject.
A simple way to depict sets visually is with a Venn diagram, also called an Euler-Venn diagram. A circle is used for the sets that are being considered, and a rectangle is used as the standard representation.
What is a Venn Diagram?Consequently, we'll talk about issues with variables two and three in this post.
Let's look at some fundamental Venn diagram formulas for two and three members.
n (A ∪ B) = n (A + B) - n (A ∪ B)
n (A ∪ B ∪ C ) = n(A) + n (B) + n (C) - n (A ∩ B) - n (B ∩ C) - n (C ∩ A) + n (A ∩ B ∩ C)
Then, where n(A) is the quantity of elements in set A, goes on.
You won't need to memorize these formulas once you've understood the notion of a Venn diagram using diagrams.
In this scenario, X is the number of elements that only belong to set A, Y is the number of elements that only belong to set B, and Z is the number of elements that both sets A and B (A + B) contain.
W is the number of objects that are not part of either set A or set B.
n(A) = x + z; n(B) = y + z; n(A B) = z; and n (A B) = x + y + z are all easily deduced from the above diagram.
w = total number of elements = x + y + z.
The Complete Question.
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A hexagon can be created with 2 parallelograms. Find
cos CAB in terms of x.
BA= CA = 10. Hint DE=BC
The answer is cos CAB = 5 × √(10² + h²) in terms of x.
What is cos CAB in terms of X?"h" denotes the parallelogram's height.
We know that the base of parallelogram A and B is 10, so the area of parallelogram A and B can be found by:
Area = base * height = 10 * h
Since parallelogram A and B make up a hexagon, their combined area must equal the area of the hexagon:
2 * (10 * h) = 6 * h * a/2
Where a is the length of one of the sides of the hexagon.
Solving for a, we get:
a = 5 * h
Next, let's find the length of DE, which is equal to BC.
We know that the height of parallelogram A is h, and the base is 10.
So, the diagonal of parallelogram A can be found using the Pythagorean theorem:
DA = √(10² + h²)
Since DE = DA, we can substitute DA with DE:
DE = √(10² + h²)
Now we can find cos CAB using the Law of Cosines:
cos CAB = (AB² + BC² - AC²) / 2 * AB * BC
AB = 10
BC = DE = √(10²+ h²)
AC = 10
So,
cos CAB = (10² + (√(10² + h²))² - 10²) / 2 * 10 * √(10² + h²)
= (√(10² + h²))² / 2 * 10 * √(10² + h²)
= 5 × √(10² + h²)
Since h is a variable, we cannot simplify the expression further.
Therefore, cos CAB = 5 × √(10² + h²) in terms of x.
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Pls help with the conditions and simplifying
Answer:
Step-by-step explanation:
[tex]\frac{1}{\sqrt{y} } (\frac{1}{\sqrt{x} -\sqrt{y} } -\frac{1}{\sqrt{x} +\sqrt{y} } )\\=\frac{1}{\sqrt{y} } (\frac{\sqrt{x} +\sqrt{y} -(\sqrt{x} -\sqrt{y} )}{(\sqrt{x} -\sqrt{y} )(\sqrt{x} +\sqrt{y} )} )\\=\frac{1}{\sqrt{y} } (\frac{\sqrt{x} +\sqrt{y} -\sqrt{x} +\sqrt{y} }{(\sqrt{x} )^2-(\sqrt{y} )^2}\\=\frac{1}{\sqrt{y} } (\frac{2\sqrt{y} }{x-y} ) \\=\frac{2}{x-y} ,x\neq y[/tex]
Boris rented a truck for one day. There was a base fee of 14.99, and there was an additional charge of 77 cents for each mile driven. Boris had to pay 204.41 when he returned the truck. For how many miles did he drive the truck?
The miles he drove the truck is, 246.
As per the given data Boris rented a truck for one day with a base of 14.99, and there was an additional charge of 77 cents for each mile driven. Boris had to pay 204.41 when he returned the truck here, we have to determine how many miles Boris drive the truck. consider that number of miles he drove be x.
let the number of miles he drove be x.
per mile the cost is $0.77
Base fee is 14.99.
0.77x + 14.99= 204.41
0.77x = 204.41-14.99
0.77x = 189.42
x = [tex]\frac{189.42}{ 0.77}[/tex]
x= [tex]\frac{190}{0.77}[/tex]
=246 miles he drove in one day.
Therefore, the miles he drove the truck is, 246.
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Can someone help me with this question please?
Answer:
40h+100 represents the amount of money it would cost to have an electrician for h hours.
Answer:
40h + 100
Step-by-step explanation:
The 100 represents the one-time fee, and the 40h represents how each hour costs 40 dollars
help!!! giving brainlist !!!
Answer:
I believe it is -0.2
Step-by-step explanation:
Because all your doing is simplifying the equation, Tell me if im wrong that way other people know
What is the vertical distance between the points C(2, -0.8) D(2,1.2)
Answer:
2 units
Step-by-step explanation:
vertical distance will be the magnitude of the difference in the 'y' coordinates
| -.8 - 1.2| = 2 units
A model of DNA is shown.
Structure 1
MMM
Which label identifies a hydrogen bond?
A. Structure 1
B. Structure 2
C. Structure 3
Structure 4
D. Structure 4
Structure 2
3
5%
Structure 3
K
A hydrogen donor and acceptor must both be present for a hydrogen bond to form.
How do you tell if a bond is a hydrogen bond?The key concepts in hydrogen bonding are;
The Hydrogen Bond Acceptor is the electronegative atom containing the lone pair electrons.The Hydrogen Bond Donor is the electronegative atom that is joined to the hydrogen.The Hydrogen Bond Donor and the Hydrogen Bond Donor must be 180 degrees apart.Typically, a strongly electronegative element like N, O, that is covalently connected to a hydrogen bond serves as the donor in a hydrogen bond.
Given that the information is incomplete, the above information shows adequate information about hydrogen bonds.
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Methadone is a synthetic drug that has been used to help people control addiction to opiates. However, according to the voter base of a governor running for re-election, Methadone use has gotten out of hand in the state. As part of their claim, the voters sent to the governor's office the following frequency distribution summarizing the daily Methadone dosages (in milligrams) of 32 patients at a state funded clinic. Daily Methadone dosage (in milligrams) 0 to 49 50 to 99 100 to 149 150 to 199 200 to 249 Frequency 6 9 10 6 1 Based on the frequency distribution, using the midpoint of each data class, estimate the mean daily Methadone dosage for the patients. For your intermediate computations, use four or more decimal places, and round your answer to one decimal place. milligrams X
Answer:
To calculate the mean daily Methadone dosage for the patients, we need to first find the midpoint of each data class, which is the average of the lower and upper bounds of the class. The data classes are:
0 to 49: Midpoint = (0 + 49) / 2 = 24.5
50 to 99: Midpoint = (50 + 99) / 2 = 74.5
100 to 149: Midpoint = (100 + 149) / 2 = 124.5
150 to 199: Midpoint = (150 + 199) / 2 = 174.5
200 to 249: Midpoint = (200 + 249) / 2 = 224.5
Next, we need to multiply the midpoint of each class by the corresponding frequency and sum these values up. This will give us the numerator of the mean formula. The formula is:
Mean = (Sum of (midpoint * frequency)) / Total frequency
So, the mean can be calculated as:
Mean = (24.5 * 6 + 74.5 * 9 + 124.5 * 10 + 174.5 * 6 + 224.5 * 1) / 32
Mean = (147 + 671 + 1245 + 1044 + 224.5) / 32
Mean = 3440.5 / 32
Mean = 107.53125
Rounding to one decimal place, the mean daily Methadone dosage for the patients is 107.5 milligrams.
Find the area of the region bounded by the line y=3x−6 and line y=−2x+8.
b) the x-axis.
pls help
B = 12/5 units
We can find the intersection point between these two lines:
y = 3x - 6
y = -2x + 8
Set these two equations equal to each other.
3x - 6 = -2x + 8
Add 2x to both sides of the equation.
5x - 6 = 8
Add 6 to both sides of the equation.
5x = 14
Divide both sides of the equation by 5.
x = 14/5
Set both equations equal to 0.
(I) 0 = 3x - 6
Add 6 both sides of the equation.
6 = 3x
Divide both sides of the equation by 3.
x = 2
Set the second equation equal to 0.
(II) 0 = -2x + 8
Add 2x to both sides of the equation.
2x = 8
Divide both sides of the equation by 2.
x = 4
Formula for the Area of a Triangle:
B = 1/2bh
Substitute 2 for b and 14/5 for h.
B = (1/2) · (2) · (12/5)
Multiply and simplify.
B = 12/5
The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.
I hope this helps! o(〃＾▽＾〃)o
Solve this equation using the most direct method
3x(x + 6) = -10
Enter your solution in the exact, most simplified form. If there are two solutions, write the answer using the ± symbol.
Answer:
(-18±[tex]\sqrt{204}[/tex])÷6
Step-by-step explanation:
Problem 3.24 ffective interest rate and PR entire compounain Ans: a. 6.66% Aruna invested Rs 150,000 eighteen months ago. Currently, the investment is worth Rs 168,925. Aruna knows the investment has paid interest every three months, but she does not know what the yield on her investment is. Compute both annual percentage rate (APR) and the effective annual rate of interest on her investment. Ans: 8%; 8.24% arehouse To finance the purchase you have
Answer:To calculate the annual percentage rate (APR) and effective annual rate of interest on Aruna's investment, we can use the following formula:
APR = (FV/PV)^(1/n) - 1
Where FV is the Future Value, PV is the Present Value, and n is the number of periods.
In this case, FV = 168,925, PV = 150,000, and n = 1.5 (since the investment was held for 18 months).
Therefore, the APR = (168,925/150,000)^(1/1.5) - 1
APR = 6.66%
The effective annual rate of interest (EAR) can be calculated using the following formula:
EAR = (1 + APR/m)^m - 1
Where m is the number of compounding periods in one year.
In this case, m = 4 (since interest is paid every 3 months).
Therefore, the EAR = (1 + 6.66%/4)^4 - 1
EAR = 8.24%
Modeling with Composite Functions
6. A store offers a 15% discount on all items and you also have a $10 coupon. Both discounts can be applied to your purchase.
a. Write a function rule, f(x) for using the coupon
b. Write a function rule, g(x) for using the 15% discount.
c. Write a function composition rule for using the $10 coupon first and then taking the 15% discount
d. Write a function composition rule for using the 15% discount first and then taking the $10 coupon.
e. Which method gives you the lowest purchase cost?
The function rules are (a) f(x) = x - 10, (b) g(x) = 0.85x, (c) g (f(x)) = 0.85x - 8.5 and (d) f (g(x)) = 0.85x - 10
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Let x be the original price of the item.
(a) You have $10 coupon.
Price of the item after applying coupon = x - 10
f(x) = x - 10
(b) There is a 15% discount.
Discounted price of the item = x - (15% × x)
= x - (0.15x)
= 0.85x
g(x) = 0.85x
(c) We have f(x) = x - 10 and g(x) = 0.85x
Price of the item when applied $10 coupon first and then taking the 15% discount is,
g (f(x)) = g(x - 10) = 0.85(x - 10) = 0.85x - 8.5
(d) Price of the item when applied 15% discount first and then taking the $10 coupon is,
f (g(x)) = f(0.85x) = 0.85x - 10
(e) We have g (f(x)) = 0.85x - 8.5 and f (g(x)) = 0.85x - 10
The price will be lower for the composite function f (g(x)) = 0.85x - 10, since there is a $10 decrease in the 0.85x.
Hence the rules for the functions are f(x) = x - 10 and g(x) = 0.85x. The composite functions are g (f(x)) = 0.85x - 8.5 and f (g(x)) = 0.85x - 10.
The price will be lower when we first apply the discount and then the coupon.
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EASY POINTS!
An art dealer earns a 12% commission for every painting she sells. How much commission does the art dealer earn from selling 3 paintings for $750 each?
$270
$1,020
$180
$90
Answer:
$270
Step-by-step explanation:
0.12 x 750 = 90
90 x 3 = 270
There are 32 Year 8 pupils in a music club, out of a total of 85 pupils.
Write this proportion as a percentage.
The proportion as a percentage is calculated as: 37.65%.
How to Write a Proportion as a Percentage?To write a proportion as a percentage, divide the numerator by the denominator and multiply by 100. The resulting decimal value is the percentage.
Therefore, to write the proportion as a percentage, we need to divide the number of Year 8 pupils in the music club by the total number of pupils and multiply by 100:
(32 / 85) x 100 = 37.65%
So, the proportion of Year 8 pupils in the music club is 37.65%.
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Find the equation for the function described below. (Let x be the independent variable and ybe the dependent variable.) The linear function whose graph has slope −4 and passes through the point (5,2)
The linear function whose graph has slope -4 and passes through the point (5, 2) is f(x) = -4x + 22
Let us assume that f(x) be a required linear function.
We know that an equation of the line passing through point (x₀, y₀) and having slope m is:
(y - y₀) = m(x - x₀)
Let (x₀, y₀) = (5, 2) and slope m = -4
So, the equation of the line would be,
(y - y₀) = m(x - x₀)
(y - 2) = -4(x - 5)
y - 2 = -4x + 20
y -2 + 2 = -4x + 20 + 2
y = -4x + 22
Let y = f(x)
f(x) = -4x + 22
So, the linear function is: f(x) = -4x + 22
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given m<1=65 degree, what is m<7?
Based on the Alternate Exterior Angles Theorem, the measure of angle 7 is 65 degrees.
What is the Alternate Exterior Angles Theorem?The Alternate Exterior Angles Theorem states that if two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent (equal in measure). In other words, the angles on the outside of the lines, on opposite sides of the transversal, have the same measure
Angles 1 and 7 are exterior angles, therefore:
m<7 = m<1
Substitute
m<7 = 65 degrees.
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2(5x + 4) + 3(2x - 1)
Answer:
16x + 5
Step-by-step explanation:
2(5x + 4) + 3(2x - 1) ← distribute both parenthesis
= 10x + 8 + 6x - 3 ← collect like terms
= (10x + 6x) + (8 - 3)
= 16x + 5
Given that LJ bisects HJK find the value of y and the lemgth of LH
Answer: y = 4 and LH = 16
Step-by-step explanation:
because of the fact that HJK is bisected by LJ, we know that LH and LK are equal. with that, we can equal 3y + 4 and 6y - 8.
3y + 4 = 6y - 8
3y + 12 = 6y
12 = 3y
y = 4
with that, we can now plug in 4 for y in 6y - 8.
6(4) - 8
24 - 8
16
Therefore, y = 4 and LH = 16.
y=3x²-5x+4 is there a relationship between the degree of a polynomial and how steep it is on the left and right edges. If it is so, what is it?
Answer:
Step-by-step explanation:
The revenue can be modeled by the polynomial function
R
(
t
)
=
−
0.037
t
4
+
1.414
t
3
−
19.777
t
2
+
118.696
t
−
205.332
where R represents the revenue in millions of dollars and t represents the year, with t = 6 corresponding to 2006. Over which intervals is the revenue for the company increasing? Over which intervals is the revenue for the company decreasing? These questions, along with many others, can be answered by examining the graph of the polynomial function. We have already explored the local behavior of quadratics, a special case of polynomials. In this section we will explore the local behavior of polynomials in general.
Multiplicity and Turning Points
Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Suppose, for example, we graph the function
f
(
x
)
=
(
x
+
3
)
(
x
−
2
)
2
(
x
+
1
)
3
.
Notice in the figure below that the behavior of the function at each of the x-intercepts is different.
Graph of h(x)=x^3+4x^2+x-6.
The behavior of a graph at an x-intercept can be determined by examining the multiplicity of the zero.
The x-intercept
x
=
−
3
is the solution to the equation
(
x
+
3
)
=
0
. The graph passes directly through the x-intercept at
x
=
−
3
. The factor is linear (has a degree of 1), so the behavior near the intercept is like that of a line; it passes directly through the intercept. We call this a single zero because the zero corresponds to a single factor of the function.
The x-intercept x=2
is the repeated solution to the equation (x−2)2=0
. The graph touches the axis at the intercept and changes direction. The factor is quadratic (degree 2), so the behavior near the intercept is like that of a quadratic—it bounces off of the horizontal axis at the intercept.
(x−2)2=(x−2)(x−2)
Ashley makes house calls. For each, she is paid a base amount and makes additional money for each hour she works. The graph below shows her pay (in dollars) versus the number of hours worked.
A) what is Ashley’s pay for a bourse call if she doesn’t work any hours?
B) what is her pay is she works 1 hour?
C)how much does her pay increase for each hour worked?
D)are the amounts given in parts (b) and (c) equal? Why or why not? Choose the best answer.
A)Yes, because the line passes through (0, 0)
B) Yes, because the line does not pass through (0, 0)
C)No, because the line passes through (0,0)
D) No, because the line does not pass through (0,0)
Ashley makes house calls. For each, she is paid a base amount and makes additional money for each hour she works. The graph below shows her pay (in dollars) versus the number of hours worked.
A) Ashley’s pay for a course call if she doesn’t work any hours is $60
B) her pay is she works 1 hour is: $90
C) her pay increases for each hour worked is: $30
D) No. Because if she works 1 hour it becomes $90 as at 0 hours her pay becomes $60.
And her pay increases for each hour is $30.
Correct option: D
What is dollar value?The amount of U.S dollars that would be produced if the appropriate foreign currency were converted into US dollars.
Currency rates, Treasury bills, and foreign exchange reserves are the three metrics used to determine the value of the US dollar. The fact is that you need to be familiar with all three in order to make informed predictions about where the dollar could go next, even if the most popular technique is through exchange rates.
This simply indicates that her set compensation (at 0 hours, even before she begins working), is $60, and that she earns $30 for each subsequent hour worked, or a $30 rise in pay overall.
Thus, correct option: D
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-12-7-2+... (to 15 terms) (r) (r 1) (1 (to 10
The 15 terms are: 2, -12, 7, -2, 20, -30, 42, -56, 72, -90, 110, -132, 156, -182, 210.
What is an A.P.?Arithmetic Progression (AP) is a numerical series in which the differences between any two successive integers is a fixed value. Arithmetic Sequence is another name for it. We will come across various key terminologies in AP, which are designated as: The first term (a), Common distinction (d), nth Term (an),The total of the first n terms (Sn).
Define progression.A progression is a sort of sequence in which a formula for the nth term may be found. The Arithmetic Progression is the most often used sequence in mathematics, using simple formulae. There are three types of progressions in mathematics. They are as follows: Arithmetic Progression (AP), Geometric Progression (GP), and Harmonic Progression (HP).
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Consider the logistic equation ˙=(1−) y ˙ = y ( 1 − y ) (a) Find the solution satisfying 1(0)=14 y 1 ( 0 ) = 14 and 2(0)=−3 y 2 ( 0 ) = − 3 .
Answer:
The logistic equation is a differential equation that describes the growth of a population over time. The solution of this equation can be found using separation of variables or other methods of solving differential equations. The general solution for the logistic equation is given by:
y(t) = y_0 * e^(rt) / (1 + (y_0 - 1)e^(rt))
Where y_0 is the initial population size, r is the growth rate, and t is time.
For the specific case given in the question, we have the initial conditions y1(0)=14 and y2(0)=-3. We can use these to find the specific solution for each case.
1(0)=14 => y1(t) = 14e^(rt) / (1 + (14 - 1)e^(rt))
2(0)=−3 => y2(t) = -3e^(rt) / (1 + (-3 - 1)e^(rt))
It is important to note that we can not find the exact value of r without additional information.
Answer:
y(t) = 1 / (1 + (-4e^(-t))
Step-by-step explanation:
The logistic equation is a nonlinear differential equation that describes how a population grows. The solution for the logistic equation is given by y(t) = 1 / (1 + (Ce^(-t)) where C is the constant of integration, which can be determined by the initial conditions.
For the first initial condition, 1(0)=14, we can substitute the initial condition into the solution to get:
y(0) = 1 / (1 + (Ce^(0)) = 1 / (1 + C) = 14
Solving for C, we get C = 13.
So the solution for the first initial condition is:
y(t) = 1 / (1 + (13e^(-t))
For the second initial condition, 2(0)=-3, we can substitute the initial condition into the solution to get:
y(0) = 1 / (1 + (Ce^(0)) = 1 / (1 + C) = -3
Solving for C, we get C = -4.
So the solution for the second initial condition is:
y(t) = 1 / (1 + (-4e^(-t))
find equivalent expressions of 3+2x-9-4x+11+5x-x
Answer:
2x + 5
Step-by-step explanation:
3 + 2x - 9 - 4x + 11 + 5x - x
2x - 4x + 5x - x + 3 - 9 + 11 (put "exes" and "non-exes" together)
-2x + 4x - 6 + 11
2x + 5
Answer: Look at the screenshot below
Hi, I am having trouble determining how to calculate the average cost per unit? Any help is greatly appreciated.
Kubin Company's relevant range of production is $16,000 to 24,500. When it produces 20,250units, it's average cost s per unit are as follows (see attached).
1) For Financial Accounting purposes, what is the total amount of product costs incurred to make 24,500 units?
2) what is the total amount of period costs incurred to sell 16,000 units?
Step-by-step explanation:]
Answer:
The total amount of product costs incurred to make 24,500 units is $208,250.
The total amount of period costs incurred to sell 16,000 units is $81,750.
Step-by-step explanation:
To determine the total amount of product costs incurred to make 24,500 units, we need to multiply the average cost per unit by the number of units produced. Since the average cost per unit is $8.50, the total product costs incurred to make 24,500 units would be:
$8.50 x 24,500 = $208,250
To determine the total amount of period costs incurred to sell 16,000 units, we need to use the information provided for the relevant range of production. The relevant range of production is $16,000 to 24,500. The period costs are fixed costs that do not change with the level of production. Since the period costs are not dependent on the level of production, the total amount of period costs incurred to sell 16,000 units would be the same as selling 24,500 units. To find the total period costs, we need to subtract the product costs from the total costs.
Total Costs = $290,000 (from the attached sheet)
Product costs = $208,250 (calculated above)
Period costs = Total Costs - Product costs = $290,000 - $208,250 = $81,750
The total amount of period costs incurred to sell 16,000 units is $81,750.
a confounding variable makes it easier to draw conclusions from a study. press space or enter to grab true in a randomized experiment the treatment and control groups do not differ in any systematic way except that they receive different treatments. press space or enter to grab true in an observational study subjects are assigned to treatment groups at random. press space or enter to grab false observational studies are generally more reliable than randomized experiments press space or enter to grab true the four main principles of randomized experiments are: (1) control (2) randomization (3) replication (4) blocking press space or enter to grab false in a double-blind study neither the investigators nor the subjects know who is getting what treatment
The four main principles of randomized experiments are:
True, True, False, True, and True
1. True: Confounding variables can make it harder to draw conclusions from a study because they can obscure the effect of the treatment being studied. Confounding variables are extraneous factors that can affect the outcome of the study and mimic or mask the effect of the treatment being studied.
2. True: In a randomized experiment, the treatment and control groups are designed to be as similar as possible in terms of all relevant factors, except for the treatment itself. This helps to ensure that any observed differences between the groups can be attributed to the treatment being studied, rather than to other factors that might affect the outcome.
3. False: Observational studies are generally considered to be less reliable than randomized experiments because they are subject to a number of biases that can affect the results. For example, observational studies often involve selection bias, in which certain groups are more likely to be included in the study, and measurement bias, in which the measurements used in the study are not accurate or reliable.
4. True: The four main principles of randomized experiments are:
control, which involves controlling for all relevant factors that might affect the outcome of the study;randomization, which involves randomly assigning subjects to treatment groups; replication, which involves repeating the experiment multiple times to increase the reliability of the results; blocking, which involves grouping subjects in a way that minimizes the impact of extraneous factors that might affect the outcome.5. True: In a double-blind study, neither the investigators nor the subjects know who is receiving which treatment. This helps to reduce the potential for bias and increase the reliability of the results, by ensuring that neither the investigators nor the subjects can influence the outcome of the study based on their knowledge of the treatment assignments.
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students deliver newspapers and magazines to houses.
One day, they have to deliver 875 newspapers and 1200 magazines.
Each student can deliver either 35 newspapers or 50 magazines in 1 hour.
Each student can only work for 8 hours.
Work out the minimum number of students needed
Answer:
Step-by-step explanation:
To determine the minimum number of students needed, we need to first determine how many newspapers and magazines each student can deliver in total (over 8 hours).
Each student can deliver 35 newspapers + 50 magazines = 85 newspapers + magazines per hour.
In 8 hours, each student can deliver 85 newspapers + magazines/hour * 8 hours = 680 newspapers + magazines.
Now, we can divide the total number of newspapers and magazines to be delivered by the number of newspapers and magazines each student can deliver in 8 hours:
875 newspapers + 1200 magazines = 2075 newspapers + magazines
2075 newspapers + magazines / 680 newspapers + magazines/student = 3 students.
Therefore, the minimum number of students needed to deliver 875 newspapers and 1200 magazines is 3 students.
A spherical gasoline tank has been drained. If the result was 65,450 cubic feet of gasoline, what was the diameter?
The required diameter of the spherical gasoline tank is given as 50 feet.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
The volume of the cylinder = 4/3πr³
4/3πr³ = 65450
r³ = 15625
r = 25 feet
Diameter = 2 × r
= 2 × 25
= 50 feet
Thus, the required diameter of the spherical gasoline tank is given as 50 feet.
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Line n intersects lines I and m, forming the angles
shown in the diagram below.
(6x + 42)
(18x-12)
Which value of x would prove | m?
✦ M
The value of x that proves that line l is parallel to line m is 4.5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Alternate interior angles are formed when two parallel lines cut by a transversal, the pair of alternate interior angles formed are congruent to each other.
Given that:
Line L is parallel to line M, hence:
6x + 42 = 18x - 12 (alternate interior angles theorem)
18x - 6x = 42 + 12
12x = 54
x = 4.5
The value of x is 4.5
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Question number 17
Show that the equation represents a sphere, and find its centre and radius.
By algebra properties, the four general equations represents the standard form of the equation of the sphere.
How to determine that a general equation represents a sphere
In this problem we find four general equations that must be checked if it represent spheres, this can be done by completing the square, an application of algebra properties, and obtaining the standard form of the formula. The standard form of a sphere is shown below:
(x - h)² + (y - k)² + (z - m)² = r²
Where:
(h, k, m) - Coordinates of the center.r - Radius of the sphere.Now we proceed to determine if each equation represents a sphere:
Case 15:
x² + y² + z² - 2 · x - 4 · y + 8 · z = 15
(x² - 2 · x) + (y² - 4 · y) + (z² + 8 · z) = 15
(x² - 2 · x + 1) + (y² - 4 · y + 4) + (z² + 8 · z + 16) = 15 + 1 + 4 + 16
(x - 1)² + (y - 2)² + (z + 4)² = 6²
Case 16:
x² + y² + z² + 8 · x - 6 · y + 2 · z + 17 = 0
x² + y² + z² + 8 · x - 6 · y + 2 · z = - 17
(x² + 8 · y) + (y² - 6 · y) + (z² + 2 · z) = - 17
(x² + 8 · y + 16) + (y² - 6 · y + 9) + (z² + 2 · z + 1) = - 17 + 16 + 9 + 1
(x + 4)² + (y - 3)² + (z + 1)² = 3²
Case 17:
2 · x² + 2 · y² + 2 · z² = 8 · x - 24 · z + 1
x² + y² + z² = 4 · x - 12 · z + 1 / 2
(x² - 4 · x) + y² + (z² + 12 · z) = 1 / 2
(x² - 4 · x + 4)² + y² + (z² + 12 · z + 36) = 1 / 2 + 4 + 36
(x - 2)² + y² + (z + 6)² = 81 / 2
(x - 2)² + y² + (z + 6)² = (9√2 / 2)²
Case 18:
3 · x² + 3 · y² + 3 · z² = 10 + 6 · y + 12 · z
x² + y² + z² = 2 · y + 4 · z + 10 / 3
x² + (y² - 2 · y) + (z² - 4 · z) = 10 / 3
x² + (y² - 2 · y + 1) + (z² - 4 · z + 4) = 10 / 3 + 1 + 4
x² + (y - 1)² + (z - 2)² = 25 / 3
x² + (y - 1)² + (z - 2)² = (5√3 / 3)²
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