Answer:
$435,400
Step-by-step explanation:
Price of one ticket: $311,000/5,000
Price of one ticket: $62.20
Price of 7000 tickets: $62.20 x 7000
Price of 7000 tickets: $435,400
The function P(m) below relates the amount of time (measured in minutes)
Steve spent on his homework and the number of problems completed.
It takes as input the number of minutes worked and returns as output the
number of problems completed.
P(m) = 12 +9
Which equation below represents the inverse function M(p), which takes the
number of problems completed as input and returns the number of minutes
worked?
OA. M(p) = 6p + 54
OB. M(p) = 6p - 54
OC. M(p) = 54p - 6
OD. M(p) = 54p + 6
The inverse function of a function f in mathematics exists a function that reverses the operation of f. The number of problems completed as input and returns the number of minutes worked exists m(p) = 6p - 54.
What is meant by inverse function?An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.
Given: P(m) = (m/6) + 9
Determine the inverse function
P(m) = (m/6) + 9
Represent P(m) as P
P = (m/6) + 9
Swap the positions of P and m
m = (p/6) + 9
We are to make p the subject.
Subtract 9 from both sides, then we get
m - 9 = (p/6) + 9 - 9
m - 9 = (p/6)
Multiply through by 6
6(m - 9) = (p/6) × 6
simplifying the above equation, we get
6(m-9) = p
6 m-54 = p
Rearranging the above equation, we get
p = 6m - 54
Swap the positions of P and m
m = 6p - 54
m(p) = 6p - 54
Therefore, the correct answer is option C. M(p)=6p - 54
The complete question is:
The function below relates the amount of time (measured in minutes) Steve spent on his homework and the number of problems completed.
It takes as input the number of minutes worked and returns as output the number of problems completed.
P(m) = (m/6)+9
Which equation below represents the inverse function M(p), which takes the number of problems completed as input and returns the number of minutes worked?
A. M(p)=54p + 6
B. M(p)=54p - 6
C. M(p)=6p - 54
D. M(p)=6p + 54
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Answer:6p-54
Step-by-step explanation:
Figure A has a perimeter of 48 m and one of theside lengths is 18 m. Figure B has a perimeter of 80 m.What is the corresponding side length of Figure B?
We have to use proportions to solve this question.
According to the given information, the perimeter of Figure A is to the sidelength of that figure as the perimeter of Figure B is to the sidelength of that figure:
[tex]\begin{gathered} \frac{48}{18}=\frac{80}{x} \\ x=\frac{80\cdot18}{48} \\ x=30 \end{gathered}[/tex]The corresponding sidelength of Figure B is 30.
I need help on this please!
Answer:
y = -2x + 2
Step-by-step explanation:
so to find the slope of the graph we must do (rise)/(run)
when we see the graph we see that when it goes DOWN 2 it also goes RIGHT 1
RISE is up or down
RUN is left or right
since it is down it is negative
so
-2 / 1
that is just -2
that is the slope
the equation for slope intercept is y = mx + b where m is the slope and b is the y intercept
so far it is y = -2x + b
the y intercept is where it crosses the y axis
that point is 2 based off of the graph
so
y = -2x + 2 is your answer
Last year, Mrs.Sclair’s annual salary was $88,441. This year she received a raise and now earns $96,402 annually. She is paid weekly. a. What was her weekly salary last year? Round to the nearest cent. b.What is Mrs.Sclair’s weekly salary this year? Round to the nearest cent. c.On a weekly basis, how much more does Mrs.Sclair earn as a result of her raise?
We have the following:
old salary: $88441
new salary: $96402
The year is approximately 52 weeks, therefore:
a. old salary for week:
[tex]\begin{gathered} \frac{88441}{52}=1700.8 \\ \end{gathered}[/tex]b. new salary for week:
[tex]\frac{96402}{52}=1853.9[/tex]c. weekly raise
[tex]1853.9-1700.8=153.1[/tex]Ziba brought 4 bottles of water to the park. Each bottle held 6 ounces of water. Ziba drank an equal number of ounces of water each hour. If she was at the park 3 hours, how many ounces of water did she drink each hour
By taking the quotient between the total volume and the number of hours, we conclude that she drinks 8 ounces per hour.
How many ounces of water did she drink each hour?
We know that Ziba has 4 bottles, each one with 6 ounces, so the total volume of water is:
V = 4*6 ounces = 24 ounces.
We know that she drinks that in 3 hours, so the amount that she drinks each hour is:
24 oz/3 = 8 oz
She drinks 8 ounces of water each hour.
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HELP ME PLEASE !!!
REASONING An absolute value function is positive over its entire domain. How many x-intercepts does the graph of the function have?
● None
01
02
O Infinite
The absolute value function can intersect a horizontal x-axis at zero, one, as well as two points.
What is meant by the absolute value function?The absolute value function is usually thought to provide the distance between two numbers on a number line. Algebraically, the output is the value without regard to sign for whatever the input value is. The corner point where the graph changes direction is the most essential characteristic of the absolute value graph. This point is depicted as the origin. When the input is zero, the graph of an absolute value function would then intersect the vertical axis.Thus, depending on the way the graph has indeed been shifted and reflected, it could or might not intersect the horizontal axis.
The absolute value function can intersect the x-axis at zero, one, or two points.
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Write the following expression in its simplest form-2/3(9/2x + 15/2)
Given the expression
-2/3(9/2x + 15/2)
Open the parenthesis;
= -2/3(9/2 x) - 2/3(15/2)
= -18x/6 - 30/6
= -3x - 5
Hence the expression in its simplest form is -3x - 5
What is the distance from Point B (-1, 11) to line y = -1/3x - 6?
Answer in simplest radical form
The distance from Point B (-1, 11) to line y = (-1 ÷ 3x) - 6 is 15.811.
The distance from the point B(-1 , 11) to the line y= (-1 ÷ 3x) - 6 is given by the distance formula d = (|Ax1 + By1 + C|) ÷ (√(A² + B²)).
Comparing the equation y= (-1 ÷ 3x) - 6 with the standard forms Ax + By+ C = 0.
It is clear that the coefficient of x, A = -1 ÷ 3.
The coefficient of y, B = -1. The constant C = -6 and the points x1 = -1 and y1 = 11.
Substituting these data in the equation the distance d = (|(-1÷3)×(-1)+ (-1)×11 + (-6)|) ÷ √((-1 ÷ 3)² + (-1)² ) solving the equation the distance d becomes,
d = 15.811.
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Proofs involving a transversal
Thus, it is clear that the lines RS and TV in the preceding diagram are parallel to each other
What are the properties of parallel lines?If you extend a set of lines indefinitely, they will remain parallel and never cross each other even though they are on the same plane. The symbol || represents the collection of parallel lines. All parallel lines are always equally spaced apart. Investigate the characteristics of parallel lines.
When two lines in a plane are stretched infinitely in both directions and do not cross, they are said to be parallel.
To solve the given question we know,
angle 1= angle 2 and lines RV // TS
angle 4= angle 3(interior angles on parallel lines are equal)
angle 1=angle 4 (vertically opposite angles are equal )
angle 1= angle 3 (angle 4=angle 1)
angle 4=angle 2( angle 1=angle 4)
Now we can see that the sum of base angles of the diagram will be 180 because
180-angle 3= angle STV
angle 4=angleSTV+180 (angle 3=angle4)
we proved that the diagram is a parallelogram because base angles of the same side are supplementary:
Therefore , we can conclude that the lines RS // TV in the preceding diagram .
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5/8p−3/4=4
A) p=95/32
B) p=26/5
C) p=38/5
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p-\frac{3}{4}=4 } \end{gathered}$}}[/tex]
Add 3/4 to both sides.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=4+\frac{3}{4} } \end{gathered}$}}[/tex]
Convert 4 to the fraction 16/4.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16}{4} +\frac{3}{4} } \end{gathered}$}}[/tex]
Since 16/4 and 3/4 have the same denominator, add their numerators to add them together.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16+3}{4} \longmapsto \ \ Add } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{19}{4} } \end{gathered}$}}[/tex]
Multiply both sides by 8/5, the reciprocal of 5/8.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19}{4}\times\left(\frac{5}{8}\right) } \end{gathered}$} }[/tex]
Multiply 19/4 by 8/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19\times8}{4\times5 }\longmapsto \ Multiply } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} } \end{gathered}$}}[/tex]
We reduce the fraction 152/20 to its minimum expression by extracting and canceling 4.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} \ \ \longmapsto \ p=\frac{152\div4}{20\div4}=\frac{38}{5} } \end{gathered}$}}[/tex]
Therefore, the answer is option C.Of the 120 families, approximately___pay more than $5710 annually for day car per child.
1) Considering a Normal Distribution, then we can write out the following:
[tex]P(X>5710)=P(X-\mu>5710-6000)=P(\frac{X-\mu}{\sigma}>\frac{5710-6000}{1000})[/tex]Note that we're dealing with probabilities.
2) Let's find out the Z-score resorting to a table, we get:
[tex]Z=\frac{x-\mu}{\sigma}=\frac{5710-6000}{1000}=-0.29[/tex]2.2) So we can infer from 1 and 2:
[tex]P(X>5710)=P(Z>-0.29)=0.6141[/tex]Notice that this distribution refers to 120 families
Need help answering all these questions for the black bird. Exponential equation for the black bird: g(x) = 2^x-8 + 1King Pig is located at (11,9)Moustache Pig is located at (10,4)
Given:
Exponential equation for the black bird is,
[tex]g(x)=2^{x-8}+1[/tex]Required:
To find the starting point of bird and graph the given function.
Explanation:
(1)
The bird starting point is at x = 0,
[tex]\begin{gathered} g(0)=2^{0-8}+1 \\ \\ =2^{-8}+1 \\ \\ =1.0039 \\ \\ \approx1.004 \end{gathered}[/tex](2)
The graph of the function is,
Final Answer
(1) 1.004
(2)
savings 50,000 in 30 years with a saving compounded monthly at an interest rate of 6%. How much would I need to deposit a month?
The amount that needs to be deposited to have a saving of $50,000 in 30 years at the given interest rate is $8,302.10.
How is the amount required to have a saving of $50,000 ?The compound interest formula is expressed as;
P = A / (1 + r/n)^nt
Where P is principal, A is amount accrued, r is interest rate is compound period and t is time elapsed.
Given the data in the question;
Accrued amount A = $50,000Interest rate r = 6%Compounded monthly n = 12Elapsed time t = 30 yearsPrincipal P = ?First, convert rate from percent to decimal.
Rate r = 6%
Rate r = 6/100
Rate r = 0.06 per year
To determine the principal, plug the given values into the formula above and solve or P
P = A / (1 + r/n)^nt
P = $50,000 / (1 + 0.06/12)^( 12 × 30 )
P = $50,000 / (1 + 0.05)³⁶⁰
P = $50,000 / (1.05)³⁶⁰
P = $8,302.10
Therefore, the principal investment is $8,302.10.
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the number 0.3333... repeats forever; therefore, its irrational
The statement is false, the number can be rewritten as:
0.33... = 3/9
So it is a rational number, not irrational
Is the statement true?Here we have the statement:
"the number 0.3333... repeats forever; therefore, its irrational"
This is false, and let's prove that.
our number is:
0.33...
Such that the "3" keeps repeating infinitely.
If we multiply our number by 10, we get:
10*0.33... = 3.33...
If we subtract the original number we get:
10*0.33... - 0.33... = 3
9*0.33... = 3
Solving that for our number we get:
0.33... = 3/9
So that number can be written as a quotient between two integers, which means that it is a rational number.
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Solve for r.
r - 15 / -1 = -4
Answer:
r=19
Step-by-step explanation:
15-r=-4
r=19
:]
I need help with this question I not sure but my answer was number 3 i for sure
To solve this problem, we have to compute the circumference of a circle of diameter:
[tex]d=840ft.[/tex]Recall that the circumference of a circle is given by the following formula:
[tex]C=d\pi,[/tex]where d is the diameter.
Therefore, the circumference of the reservoir is:
[tex]C=\frac{22}{7}*840ft=2640ft.[/tex]Answer:[tex]2640ft.[/tex]Solve this system of equations usingthe substitution method.y = x + 9y = -4x – 612] [UN
The given system of equations is
[tex]\begin{gathered} y=x+9\rightarrow(1) \\ y=-4x-6\rightarrow(2) \end{gathered}[/tex]We will substitute y in equation (2) by equation (1)
[tex]x+9=-4x-6[/tex]Now, add 4x to both sides
[tex]\begin{gathered} x+4x+9=-4x+4x-6 \\ 5x+9=-6 \end{gathered}[/tex]Subtract 9 from both sides
[tex]\begin{gathered} 5x+9-9=-6-9 \\ 5x=-15 \end{gathered}[/tex]Divide both sides by 5
[tex]\begin{gathered} \frac{5x}{5}=\frac{-15}{5} \\ x=-3 \end{gathered}[/tex]Substitute x by -3 in equation (1) to find y
[tex]\begin{gathered} y=-3+9 \\ y=6 \end{gathered}[/tex]The solution of the system is (-3, 6)
Rewrite the expression (17x3 – 12x2 + 6x - 4)/(x – 1) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor, using the synthetic division method.
Given that
The equation is
[tex]\frac{17x^3-12x^2+6x-4}{x-1}[/tex]and we have to convert it into the form of
[tex]\begin{gathered} q(x)+\frac{r(x)}{b(x)} \\ where\text{ q\lparen x\rparen is quotient, r\lparen x\rparen is remainder, and b\lparen x\rparen is divisor.} \end{gathered}[/tex]a. Find the value of x given that r ll s.The measure of angle 1 = (63-x)The measure of angle 2 = (72-2x)b. Find the measure of angle 1 and the measure of angle 2.
In the given illustration, angle 1 and angle 2 are corresponding angles.
Note that corresponding angles in parallel lines are congruent.
angle 1 measures (63 - x)
angle 2 measures (72 - 2x)
Since both angles are congruent with each other, equate the angles :
[tex]\begin{gathered} 63-x=72-2x \\ \text{Solve for x, put the variables to the left side and the constant to the right side :} \\ -x+2x=72-63 \\ x=9 \end{gathered}[/tex]The measure of angle 1 will be :
[tex]63-9=54[/tex]The measure of angle 2 will be :
[tex]72-2(9)=54[/tex]ANSWERS :
a. x = 9
b. angle 1 = 54 degrees
angle 2 = 54 degrees
Randy has $12 which he decides to put into his savings account. Every week Randy does chores to earn a $6 allowance which he continues to save and put into his savings account.Like Randy, Becky decides to be more responsible with her money and also save her money. Right now she owes her parents $8. Becky also earns $7 a week for doing chores, If both Randy and Becky save up beginning today whose savings account would reach $50first?A. RandyB. BeckyC. They would reach $50 at the same time.D. There is not enough given information to determine who will save up $50 first
Randy's initial money = $12
Randy's earnings per week = $6
Becky's initial money = -$6 (she owes )
Becky's earnings per week = $7
Number of weeks: x
The equation for each:
• Randy:
50 = 12 + 6x
• Becky:
50 = -6 + 7x
Solve each for x:
Randy:
50= 12 + 6x
50-12 = 6x
38 = 6x
38/6=x
x= 6.3
Becky:
50= -8 + 7x
50+8 =7x
58=7x
58/7=x
x= 8.28
Randy will take 6.33 weeks and Becky 8.28 weeks.
Answer:
A. Randy
What is the sum of the first five terms in this series? 6 - 6/3+6/9-6/27+•••
A 61/81
B 16
C 122/27
D 20/3
The sum of the first five terms in this series is 4 14/27.
What are fractions?Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It specifies how many identically sized pieces of the entire event or collection were collected. The denominator is the quantity listed below the line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed. A fraction can be expressed in one of three different ways: as a fraction, a percentage, or a decimal. The first and most popular way to express a fraction is in the form of the letter ab. Here, a and b are referred to as the numerator and denominator, respectively.
The first five terms
6
-6/3
6/9
-6/27
+6/81
The first thing to do is change all the fractions denominators to 81.
Sum = 6*81/81 - 6(27)/81 + 6 × 9/81 - 6 × 3/81 + 6/81
Now add
Sum = 366/81
Sum = 4 14/27
Sum = 4.5185
Recall the first term. It was increased by 6 × 81/81. Nothing is affected by the 81 over 81 in terms of value. 6 × 81/81 remains 6. It merely makes combining it with the other members of the series simpler.
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At the local food stand, the vendor sells small drinks for $1.25 each and large drinks for $2.50 each. They sold 155 drinks today and made $265. How many small drinks and how many large drinks did they sell?
Answer:
98 small drinks and 57 large drinks.
Explanation:
Let's call x the number of small drinks and y the number of large drinks.
If they sold 155 drinks, we can write the following equation:
x + y = 155
In the same way, they made $265, so
1.25x + 2.50y = 265
Because each small drink cost $1.25 and each large drink cost $2.50.
Now, we can have the following system of equations
x + y = 155
1.25x + 2.50y = 265
Solving the firs equation for y, we get:
x + y - x = 155 - x
y = 155 - x
Replacing this on the second equation:
1.25x + 2.50y = 265
1.25x + 2.50(155 - x) = 265
Then, solving for x, we ge:
1.25x + 2.50(155) - 2.50(x) = 265
1.25x + 387.5 - 2.50x = 265
-1.25x + 387.5 = 265
-1.25x + 387.5 - 387.5 = 265 - 387.5
-1.25x = -122.5
-1.25x/(-1.25) = -122.5/(-1.25)
x = 98
Finally, we can find the value of y replacing x = 98
y = 155 - x
y = 155 - 98
y = 57
Therefore, they sell 98 small drinks and 57 large drinks.
I need help on this question please?
parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.
What is a parabola in math?
Drawing a parabola for the quadratic function f(x) = ax2 + bx + c results in a U-shaped curve.When an is smaller than zero, the parabola's graph is downward (or opens downward).When the value of an is greater than 0, the parabola's graph ascends (or opens up). The locus of points in that plane that are equally spaced apart from the direct x and the focus is known as the parabola.A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.A parabola's general equation is written as y = a(x - h)2 + k or x = a(y - k)2 + h.Vertex here is indicated by (h, k).The typical form is y = a(x - h)2 + k.-9(x_6)²_1
= -9(x-6)1
=-9x+54
Differentiate x
-9
-9(x-6)²
Subtract
d/dx(-9(x-6)
Calculate x-6
d/dx (-9x+54)
-9x1-1
-9x
=-9
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Harriet sells prints of her photographs, and is deciding what her minimum order should be during a sale. The equation that relates to her profit, y, from a minimum order of size x is 12x - 4y = 48.
Part A
What are the x-intercept and the y-intercept of the graph of her profit?
A. X-intercept: 3; y-intercept: -12
B. X-intercept: 4; y-intercept: 12
C. X-intercept: 4; y-intercept: -12
D. X-intercept: 3; y-intercept: 12
Part B
What should her minimum order size be, to make a profit?
Consider the given linear equation,
[tex]12x-4y=48[/tex]PART A
Substitute y=0 to obtain the x-intercept,
[tex]\begin{gathered} 12x-4(0)=48 \\ 12x=48 \\ x=4 \end{gathered}[/tex]Thus, the x-intercept is 4 .
Substitute x=0 to obtain the y-intercept,
[tex]\begin{gathered} 12\mleft(0\mright)-4y=48 \\ -4y=48 \\ y=-12 \end{gathered}[/tex]Thus, the y-intercept is -12 .
Therefore, option C is the correct choice
PART B
The linear equation can also be written as,
[tex]\begin{gathered} 4y=12x-48 \\ y=\frac{12}{4}x-\frac{48}{4} \\ y=3x-12 \end{gathered}[/tex]The minimum limit to make a profit can be calculated as,
[tex]\begin{gathered} y>0 \\ 3x-12>0 \\ 3x>12 \\ x>\frac{12}{3} \\ x>4 \end{gathered}[/tex]Note that the order of photograph must be an integer. The next integer after 4 is 5.
So the minimum order size to make a profit should be 5.
the graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the domain of the function.
The domain of the function for the volume of the liquid = 0 ≤ V ≤ 7.5 liters.
What is domain of a function?The domain of a function is the complete set of possible values of the independent variable.
Also a domain of a function refers to "all the values" that go into a function.
From the graph the domain of the function of the volume of the of liquid in the bucket is calculated as follows;
The minimum value of the volume of liquid in the bucket = 0
The maximum value of the volume of liquid in the bucket = 7.5 liters
The domain of the function for the volume (V) of the liquid = {0, 1, 2, 3, 4, 5, 6, 7.5 liters}
0 ≤ V ≤ 7.5 liters
Thus, the domain of the function or independent variables that satisfies the function include natural numbers between 0 to 7.5 liters. That is the domain of the function is {0, 1, 2, 3, 4, 5, 6, 7.5 liters}.
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Enter the solution to the inequality below. Enter your answer as an inequality.
Use =< for and >= for >
√x ≥ 17
Answer here
SUBMIT
The solution of the inequality is [tex]x \geq 289[/tex].
What is inequality?
Inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ( [tex]\neq[/tex]) " to indicate that two values are not equal. But several inequalities are utilised to compare the numbers, whether it is less than or higher than.
The given inequality is, [tex]\sqrt{x} \geq 17[/tex]
Taking square on both sides, we get
[tex]x\geq 289[/tex].
Therefore, the solution of the inequality is [tex]x \geq 289[/tex].
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crate A exerts a force of 8320N and a pressure of 64N/cm2. crate B exerts a force of 9860N and a pressure of 29N/cm2. find the difference between the base areas of the crates in cm2
Answer:
difference in base areas = 210 cm²
Step-by-step explanation:
In order to calculate the difference in the base areas of the crates, we first need to find the base area of each crate.
To calculate the base area, we can use the formula for pressure and rearrange it to make area the subject:
[tex]\boxed{Pressure = \frac{Force}{Area}}[/tex]
⇒ [tex]Area = \frac{Force}{Pressure}[/tex]
Therefore:
•Base area of crate A = [tex]\mathrm{\frac{8320 \ N}{64 \ N/cm^2}}[/tex]
= 130 cm²
• Base area of crate B = [tex]\mathrm{\frac{9860 \ N}{29 \ N/cm^2}}[/tex]
= 340 cm²
Now that we know the base areas of each crate, we can easily calculate the difference between them:
difference = 340 cm² - 130cm²
= 210 cm²
If triangles MNP is an equilateral triangle, find x and the measure of each side.
The value of x = 13
Each side of the equilateral triangle is: 27 units.
What is an equilateral Triangle?A triangle is classified or defined as an equilateral triangle if all its sides are of the same length. This means, all equilateral triangles have side lengths that are congruent.
Since triangle MNP is said to be an equilateral triangle, all its sides would be equal to each other. Therefore:
MN = NP = MP
Given the following:
MN = 4x - 25
NP = x + 14
MP = 6x - 51
Thus:
MN = NP
Substitute
4x - 25 = x + 14
4x - x = 25 + 14
3x = 39
x = 39/3
x = 13
MN = 4x - 25 = 4(13) - 25 = 27
MN = NP = MP
NP = 27
MP = 27
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You are told that a 95% confidence interval for the population mean of a normally distributed variable is 17.3 to 24.5. if the population was 76, what was the sample standard deviation?
The sample standard deviation of the population with confidence interval of 95% is 13.57
What is standard deviation?Standard deviation gives a value that measures how much the given value differ from the mean.
How to find the sample standard deviationGiven data form the question
95% confidence interval
population mean of a normally distributed variable is 17.3 to 24.5
population was 76
Definition of variables
confidence interval = CI = 95%
mean = X = 17.3 to 24.5
taking the average, X = 21.45
standard deviation = SD = ?
Z score = z = 1.96
from z table z score of 95%confidence interval = 1.96
sample size = n = 76
The formula for the confidence interval is given by
[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex] OR [tex]X-Z\frac{SD}{\sqrt{n} }[/tex]
[tex]24.5=21.45+1.96\frac{SD}{\sqrt{76} }[/tex]
[tex]24.5-21.45=1.96\frac{SD}{\sqrt{76} }[/tex]
[tex]3.05=1.96\frac{SD}{\sqrt{76} }[/tex]
[tex]\frac{3.05}{1.96} =\frac{SD}{\sqrt{76} }[/tex]
[tex]1.5561 =\frac{SD}{\sqrt{76} }[/tex]
SD = √76 * 1.5561
SD = 13.56577
SD ≈ 13.57
The standard deviation is solved to be 13.57
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calculate the area of this trapiziuem
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