You have 72 square feet of material to build a rectangular box.
The length is twice the width and there is no top.
What values for W and L and H will create a box that encloses the maximum volume using the material you have?
W = ?
L = ?
H = ?
Answers
For the given conditions, the length of box=6.92 feet, width of box=3.46 feet and height of box=2.31 feet.
What is volume?Each object in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's capacity.
Here,
area of material=72 feet²
V=lbh
l=2b
72=lb+2lh+2bh
substitute l as 2b,
72=2b²+4bh+2bh
36=b²+3bh
3bh=36-b²
h=(36-b²)/3b
v=lbh
v=2b*b*(36-b²)/3b
v=2b*(36-b²)/3
=(72b-2b³)/3
differentiate the v,
v'=1/3(72-6b²)
v'=0
72-6b²=0
6b²=72
b²=12
b=√12
b=3.46 feet
l=2b=6.92 feet
h=(36-b²)/3b
=(36-12)/3*3.46
h=2.31 feet
The box measures 6.92 feet long, 3.46 feet wide, and 2.31 feet tall under the specified circumstances.
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Answer:
[tex]W=2\sqrt{3}=3.46\; \sf ft\;(2\;d.p.)[/tex]
[tex]L=4\sqrt{3}=6.93\; \sf ft\;(2\;d.p.)[/tex]
[tex]H = \dfrac{4\sqrt{3}}{3}=2.31\; \sf ft\;(2\;d.p.)[/tex]
Step-by-step explanation:
If the length is twice the width:
W = widthL = 2W = lengthH = heightSurface area of the box
[tex]\implies SA = WL + 2WH + 2LH[/tex]
[tex]\implies SA = W(2W) + 2WH + 2(2W)H[/tex]
[tex]\implies SA = 2W^2 + 2WH + 4WH[/tex]
[tex]\implies SA = 2W^2 + 6WH[/tex]
If the surface area is 72 ft²:
[tex]\implies 2W^2 + 6WH = 72[/tex]
[tex]\implies 6WH = 72 - 2W^2[/tex]
[tex]\implies H = \dfrac{72 - 2W^2}{6W}[/tex]
[tex]\implies H = \dfrac{36 - W^2}{3W}[/tex]
Volume of the box
[tex]\implies V = LWH[/tex]
[tex]\implies V = (2W)WH[/tex]
[tex]\implies V = 2W^2H[/tex]
Substitute the found expression for H into the formula for volume:
[tex]\implies V = 2W^2\left(\dfrac{36 - W^2}{3W}\right)[/tex]
[tex]\implies V = \dfrac{2W^2(36 - W^2)}{3W}[/tex]
[tex]\implies V = \dfrac{2W(36 - W^2)}{3}[/tex]
[tex]\implies V = \dfrac{72W - 2W^3}{3}[/tex]
[tex]\implies V =24W-\dfrac{2}{3}W^3}[/tex]
To find the value of W when the volume is at its maximum, first differentiate the equation for volume with respect to W:
[tex]\implies \dfrac{\text{d}V}{\text{d}W}=24-2W^2[/tex]
Now set the derivative to zero and solve for W:
[tex]\implies 24-2W^2=0[/tex]
[tex]\implies 2W^2=24[/tex]
[tex]\implies W^2=12[/tex]
[tex]\implies W=\sqrt{12}[/tex]
[tex]\implies W=2\sqrt{3}[/tex]
As length is twice the width:
[tex]\implies L=2 \cdot 2\sqrt{3}[/tex]
[tex]\implies L=4\sqrt{3}[/tex]
To find H, substitute the found value of W into the expression for H:
[tex]\implies H = \dfrac{36 - W^2}{3W}[/tex]
[tex]\implies H = \dfrac{36 - (2\sqrt{3})^2}{3(2\sqrt{3})}[/tex]
[tex]\implies H = \dfrac{36 - 12}{6\sqrt{3}}[/tex]
[tex]\implies H = \dfrac{24}{6\sqrt{3}}[/tex]
[tex]\implies H = \dfrac{4}{\sqrt{3}}[/tex]
[tex]\implies H = \dfrac{4\sqrt{3}}{3}[/tex]
Related Questions
Which graph represents the function f(x) = 4/x
Answers
Answer:
Step-by-step explanation:
Hunter is going to see a movie and is taking his 4 kids. Each movie ticket
costs $12 and there are an assortment of snacks available to purchase for $5
each. How much total money would Hunter have to pay for his family if he
were to buy 4 snacks for everybody to share? How much would Hunter have
to pay if he bought a snacks for everybody to share?
Answers
Answer:
$80
Step-by-step explanation:
hunter+ kid 1+kid 2+kid 3+kid 4= 60 dollars just for tickets
4 snacks= 20 dollars for snacks
$60+$20=$80
PLEASE MARK BRAINIEST
Use the following model to answer the question.
Which division problem is shown by the model?
OA. 0.66÷3= 0.22
O B. 0.663 = 0.26
OC. 0.78÷3= 0.62
www
D. 0.78÷3= 0.26
D
G
Answers
Option D is correct answer, The given model in the picture shows the division problem as: 0.78 ÷ 3 = 0.26.
What is division?
Along with addition, multiplication, and subtraction, division is one of the four basic mathematical operations. The act of separating anything into smaller groups so that each one has the same amount of items is known as division. It is a mathematical operation that is used to distribute and group things equally.
we can count that, there are 26 cubic blocks in each square in the picture,
10 each are vertically in two rows and 6 are horizontally present.
And there are total of 3 such squares present each with 26 cubic blocks.
So these all totals to 78 cubic blocks which is divided in 3 squares and in each squares there are 26 cubic blocks.
Therefore, the division problem representing this can be written as:
0.78 ÷ 3 = 0.26
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2. [5 pts] On a certain route, an airline carries 6,000 passengers per month, each paying $200. A market
survey indicates that for each $1 increase in the ticket price, the airline will lose 100 passengers.
Express the number of passengers per month, N, as a function of the ticket price, x. (Assume x ≥ 200.)
Answers
For the given passengers per month 6,000 paying $200 each with $1 increase in the ticket price with 100 lose passengers , then the number of passengers per month N as a function of the ticket price x :
N(x) = 26,000 - 100x where x ≥ 200.
As given in the function,
Number of passengers carried by airlines per month = 6,000
Price of ticket of each passenger = $200
For each $1 increase in the ticket price lose of 100 passengers
Let N(x) be the function representing the number of passengers
And x represents the price of the ticket where x ≥ 200.
Required function to represent the number of passengers is given by :
N(x) = 6,000 -100 ( x -200)
⇒ N(x) = 6,000 -100x + 20,000
⇒ N(x) = 26,000 -100x where x ≥ 200
Therefore, for the given passengers per month 6,000 paying $200 each with $1 increase in the ticket price with 100 lose passengers , then the number of passengers per month N as a function of the ticket price x :
N(x) = 26,000 - 100x where x ≥ 200.
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What is the equation for the parabola graphed below
Answers
Answer:
[tex]y = x^2 - 2x -1[/tex]
Step-by-step explanation:
General Form of a parabola :
[tex]y = a (x - h)^2 + k[/tex]
Solving :
h and k refer to the point of the vertex. In this case, it's (1, -2), so :
[tex]y = a(x - 1)^2 - 2[/tex]
Plug in values for x and y. In this case, they're (0, -1), so :
[tex]-1 = a(0 - 1)^2 - 2\\-1 =a(1) - 2\\1 = a[/tex]
Plug in all values :
[tex]y = ( x - 1)^2 -2[/tex]
Further simplifying :
[tex]y = ( x - 1 )^2 - 2 \\y = (x^2-2x + 1) - 2\\y = x^2 - 2x -1[/tex]
someone please help tysm
Answers
Among the equations and inequality the true expression is 1 / 3 × 9 = 3.
How to solve inequality and equation?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Therefore, let's check the inequality that is true.
Hence,
1 / 4 × 28 > 8
28 / 4 > 8
7 > 8 (false)
1 / 6 × 48 < 5
48 / 6 < 5
8 < 5 (False)
1 / 3 × 9 = 3
9 / 3 = 3
3 = 3(True)
1 / 5 × 25 = 125
25 / 5 = 125
5 ≠ 125(False)
1 / 6 × 24 > 9
24 / 6 > 9
4 > 9 (False)
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PLEASE ANSWER!!!! WILL GIVE BRAIN THINGY
Answers
Answer:
No solutions
Step-by-step explanation:
-5y+7/2y=-5-3/2y-4
+3/2y. +3/2y
-5y+3/2y+7/2y=-5-4
-5y+10/2y=-9
-5y+5y=-9
0=-9
No solutions
Hopes this helps please mark brainliest
Lim x->1 sinx - sin1/x-1
Answers
The limit Lim x→1 (sinx - sin1)/(x - 1) = cos1
What is the limit of a function?The limit of a function f(x) as x tends to a is the value of the function f(x) as x tends to a. It is written as [tex]\lim_{x \to a} f(x) = L[/tex]
How to find the given limit of the function?GIven that we require the limit given as [tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1}[/tex]
So, substituting the value of x = 1 into the given equation, we have that
[tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = \frac{sin1 - sin1}{1 - 1} \\= \frac{0}{0}[/tex]
Since 0/0 is one of the inderterminate forms, we use the L'hopital's rule to find the limit of the given function.
What is L'hopital's rule?L'hopital's rule states that if [tex]\lim_{x \to a} f(x) = \lim_{x \to a} g(x) = 0[/tex] and f'(x) and g'(x) exist then [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]
Let the variables be
f(x) = sinx - sin1 and g(x) = x - 1So, since we know that
[tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = \frac{0}{0}[/tex],
So, [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]
So, we differentiate both the numerator and denominator and find the limit.
So,
[tex]\lim_{x \to 1} \frac{f'(x)}{g'(x)} = \lim_{x \to 1} \frac{\frac{d(sinx - sin1)}{dx} }{\frac{d(x - 1)}{dx} } \\= \lim_{x \to 1} \frac{cosx - 0}{1 - 0} \\= \lim_{x \to 1}cosx \\= cos1[/tex]
So, [tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = cos1[/tex]
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if parallel lines are cut by transversal then there interior angles on the same side of the transversal are blank.
Answers
Anlges on the same side of the transversal add up to 180 degrees.
What is Transversal?
A transversal is a line in geometry that connects two lines in the same plane at two separate places. Transversals help determine if two or more lines in the Euclidean plane are parallel.
Solution:
Using the property of Lineaar Pair Angle the Interior Angles on the same side of the Transversal add up to 180 degrees.
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He purchases a total of 150 containers of popcorn to sell. After he sells 15 containers, he will make a total profit, after his upfront costs, of $5.50. Cassidy’s profit, after upfront costs, can be modeled by a linear function in the form y=mx+b.
What is Cassidy’s profit if he sells all of the popcorn?
HInt:Substitute 150 for x to find the profit if all the popcorn is sold.
Answers
If Cassidy sells all of the popcorn, his profit would be equal to $208.00.
What is the slope-intercept form?Mathematically, the slope-intercept form of a line can be modeled by using this linear function:
y = mx + b
Where:
m represents the slope.x and y are the points.b represents the y-intercept.How to determine Cassidy’s profit?In order to determine Cassidy’s profit, we would have to calculate the cost of the containers of popcorn by using this mathematical expression:
Note: the price tag for a container of popcorn is one dollar and fifty cents.
Cost of containers = revenue - total profit
Cost of containers = 1.50(15) - 5.50
Cost of containers = 22.5 - 5.50
Cost of containers = $17.00
Therefore, the linear function which models Cassidy’s profit is given by:
y = 1.50x - 17
If Cassidy sells all of the popcorn, his profit is given by:
Cassidy’s profit, y = 1.50x - 17
Cassidy’s profit, y = 1.50(150) - 17
Cassidy’s profit, y = 225 - 17
Cassidy’s profit, y = $208.00
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Complete Question:
Cassidy is selling popcorn for a fundraiser sale at the price shown.
A photo of a container of popcorn is shown. The price tag reads one dollar and fifty cents.
He purchases a total of 150 containers of popcorn to sell. After he sells 15 containers, he will make a total profit, after his upfront costs, of $5.50. Cassidy’s profit, after upfront costs, can be modeled by a linear function in the form y=mx+b.
What is Cassidy’s profit if he sells all of the popcorn?
HInt: Substitute 150 for x to find the profit if all the popcorn is sold.
The height (in feet) of a falling object with an initial velocity of 48 feet per
second launched straight upward from the ground is given by
h(t) =
16t2 + 48t where
is time (in seconds). What iS the average rate of
change of the height as a function of time from
= 1 to
2
Answers
The average rate of change of the height as a function of time from 1 to 2 is 96
Rate of change
Rate of change defines the ratio that compares the change in values of the y variables to the change in values of the x variables.
Given,
The height (in feet) of a falling object with an initial velocity of 48 feet per second launched straight upward from the ground is given by h(t) = 16t² + 48t where is time (in seconds).
Here we need to find the average rate of change of the height as a function of time from 1 to 2.
In order to find the average rate of change we need to find the value for the time 1 and time 2.
For, that we have to apply the value on the function,
First, we have to apply the value of t as 1, then we get the value of the function as,
h(1) = 16(1)² + 48(1)
h(1) = 16 + 48
h(1) = 64
Now, we have to apply the value of t as 2, then we get,
h(2) = 16(2)² + 48(2)
h(2) = (16 x 4) + 96
h(2) = 64 + 96
h(2) = 160
Therefore, the average rate of change is,
=> rate of change = (160 -64) / 2 - 1
=> rate of change = 96
Therefore, the average rate of change from 1 to 2 is 96.
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Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −3, ordered pair: (−5,3)
Answers
Answer:
[tex] \huge{ \boxed{y = - 3x - 12}}[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is given by
[tex]y = mx + c[/tex]
where
m is the slope
c is the y intercept
From the question
m = -3
In order to find c we substitute the point (−5,3) into the equation y = mx + c
We have
[tex]3 = - 3( - 5) + c \\ 3 = 15 + c \\ c =3 - 15 \\ c = - 12 [/tex]
We now substitute c and m into the main equation
We have the final answer as
[tex]y = - 3x - 12[/tex]
Hope this helps you
Which point below is a solution to the equation y = 2x − 5?
(1, -3)
(4, 2)
(-1, -5)
(2, 0)
Answers
Sorry I don't have the answer but I can rule out 2.
Step-by-step explanation:
4,2 and 2,0 are not going to be correct because I got them wrong on a quiz I had 2 attempts to take.
So its either 1,-3 or -1,-5.
Hope this helps you.
write the mixed number 4 2/5 as an improper fraction
Answers
Answer:
[tex]\frac{22}{5}[/tex]
Step-by-step explanation:
To write a mixed number as an improper fraction, you start by converting the "number part" into a fraction.
For example, in this problem 4 is the number part, and we want to rewrite 4 as fraction with a denominator of 5. To do this, we multiply four by 5, which is twenty and put this over 5: [tex]\frac{20}{5}[/tex]. This would be a fraction representing 4(you can check through division).
Next, we need to add [tex]\frac{2}{5}[/tex] to this. [tex]\frac{2}{5} +\frac{20}{5}[/tex] would just be [tex]\frac{22}{5}[/tex] because 20 + 2 = 22.
Naomi is going to invest $78,000 and leave it in an account for 7 years. Assuming the
interest is compounded daily, what interest rate, to the nearest hundredth of a
percent, would be required in order for Naomi to end up with $91,000?
Answers
In order to get the total amount $91,000 at the end of the 7 year, the interest rate is 2.2% on compound interest basis.
Compound Interest:
The general form to calculate the compound interest is written as,
A = P(1 + r/n)ⁿˣ
where
A = Accrued amount (principal + interest)
P = Principal amount
r = Annual nominal interest rate as a decimal
n = number of compounding periods per unit of time
x = time in decimal years
Given,
Naomi is going to invest $78,000 and leave it in an account for 7 years. Assuming the interest is compounded daily.
Here we need to find the nearest hundredth of a percent, would be required in order for Naomi to end up with $91,000.
Here we have to solve for rate r as a decimal
[tex]r = n[(A/P)^{1/nt} - 1][/tex]
r = 365 × [(91,000.00/78,000.00)1/(365)(7) - 1]
r = 0.022022202
Then convert r to R as a percentage
R = r * 100
R = 0.022022202 * 100
R = 2.202%/year
Therefore, the interest rate required to get a total amount of $91,000.00 from compound interest on a principal of $78,000.00 compounded 365 times per year over 7 years is 2.202% per year.
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1. Fourteen cars were randomly chosen at a used car lot. The age of each car and its sale price are shown in
the following table.
Answers
Answer: $10,252.87
Step-by-step explanation:
Based on the linear model of data, the price of the car that is 10 year old is approximately 10,000.
Linear model.
Basically, the linear model describes the relationship between a dependent variable, y, and one or more independent variables, X. Where the dependent variable is also called the response variable. And the independent variables are also called explanatory or predictor variables.
Given,
Here we have the table of data that contains the fourteen cars were randomly chosen at a used car lot and the age of each car and its sale price.
Now, we have to find the sale price for the 10 year old car.
In order to find the price of the 10 year old car, we have to plot these given table on the graph.
Then we get the graph like the following.
By looking at the graph, the sales price of the 10 year old car is predicted as approximately 10,000,
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You invest $6000 in a restaurant. The investment has a return of 12%. How
much do you receive for your investment after 30 months?
Answers
The return received after 30 months on an investment of $6000 will be $1800.
According to the question,
We have the following information:
You invest $6000 in a restaurant. The investment has a return of 12% per year.
We know that the following formula is used to find the simple interest on the amount:
Simple interest = principal*rate*time/100
Now, we have the following values in this case which we will put in the formula:
Principal = $6000
Rate = 12%
Time = 2.5 years
Simple interest = (6000*12*2.5)/100
Simple interest = $1800
Hence, the amount received after 30 months on an investment of $6000 will be $1800.
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A submarine descends -3.5 meters per minute. How far will the submarine descend in 8 minutes?
How do you know your answer will be negative?
Answers
Answer:
-28 meters
Step-by-step explanation:
The speed of the submarine = (-3.5) per minute
Since it's descending, we know the answer will be negative.
The distance covered by the submarine is 8 minutes = (-3.5) x 8 = -28 meters.
Answer:
28
Step-by-step explanation:
-3.5*8
(100 POINTS AND BRAINLYEST JUST PLEASE ANSWER)
1.) An algae bloom is threatening to cover Grand Lake St. Mary’s near Celina, Ohio. The EPA needs to calculate the surface area of the lake to treat the algae bloom. Estimate the area of the irregular shape.
A) Draw on the map to show what method was used to find the area of the lake. (2 points)
B) Show work to estimate the area of the lake in square units. Attach additional paper if necessary. (2 points)
C) Each unit on the grid is 0.25 miles. Find the actual estimate of the area of the lake. (2 points)
Answers
The area of the irregular shape is 288 sq. units
Given,
An algae bloom is threatening to cover Grand Lake St. Mary’s near Celina, Ohio.The EPA needs to calculate the surface area of the lake to treat the algae bloomWe have to estimate the area of the irregular shape;
Here,
The shape can be broken down into a trapezoid, a rectangle, and a triangle
The area of the trapezoid = 1/2 × 12 × 9 × (7 + 10) = 76.5 sq. unitsThe area of the rectangle = 7 × 20 = 140 sq. unitsThe area of the triangle = 1/2 × 11 × 13 = 71.5 sq. unitsThe total area = 76.5 + 140 + 71.5 = 288 sq. units
Therefore,
The area of the irregular shape is 288 sq. units
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calculate the area of this trapezium
Answers
Answer:
Step-by-step explanation:
Let the trapezium be B.
Draw a line from the top of the trapezium to it's base and call the triangle formed B.
The base of is 2cm (8cm - 6cm
The area of the triangle = 40cm² ( 5cm x 4cm x 2cm)
Area of the trapezium =. ½ (base x height)
. = 18cm²
Add area of trapezium and triangle.
= 40cm² + 18cm² = 58cm²
.
If two dice are rolled one time, find the probability of getting these results. Show all possible combinations. Express the probability as a fraction of 36
A 3 on one die or on both dice
A sum greater than or equal to 10
Answers
Step-by-step explanation:
any particular result with 2 dice has a probability of
1/6 × 1/6 = 1/36
a 3 on one die or both simply means at least one 3.
so, if all the 36 different outcomes we are looking at
3 1
3 2
3 3
3 4
3 5
3 6
1 3
2 3
4 3
5 3
6 3
the 3 3 combination can be counted only once !
so, we have 11 desired outcomes out of the possible 36.
so, the probability of getting at least one 3 is
11/36
the sum of at least 10 means the corresponding cases
4 6
5 5
5 6
6 4
6 5
6 6
in this case we don't need to turn this around, because it would be exactly the same outcomes again, and we don't want to count them twice.
so, we have 6 desired outcomes of the 36.
the probability of that is
6/36 = 1/6
The following inequalities form a system.
y is greater than or equal to two-thirds times x plus 2
y is less than negative one-third times x plus 1
Which ordered pair is included in the solution to this system?
(−6, −3)
(−6, −2)
(−6, 3)
(−6, 4)
Answers
From the graph, the ordered pair that is included in the solution to the given system is (-6, -2). The correct option is the second option (−6, −2)
Solving system of linear inequalities using graphFrom the question, we are to determine the ordered pair that is included in the solution to the given system of inequalities
The given system of inequalities is
y ≥ 2/3(x) + 2
y < -1/3(x) + 1
To determine the ordered pair that is included in the solution, we will graph the given system of linear inequalities.
The graph of the system of linear inequalities is given below.
From the graph, we can observe that (-6, -2) is a solution to the given system of linear inequalities.
Hence, the ordered pair that is a solution is (-6, -2)
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Answer:
Option B: (-6, -2)
Step-by-step explanation:
i took the test xx
Emma recorded the weight of her kitten in ounces on certain days for 24 days. The data are shown in the scatterplot.
Answers
Answer:
can you show me it so i can help
Step-by-step explanation:
NO LINKS!! Please help me with the Angle Proofs Part 3
Answers
Answers in bold
GivenDefinition of complementaryGivenDefinition of congruenceVertical anglesDefinition of congruenceSubstitution propertyDefinition of complementary==============================================
Explanation:
Always start with what is given. The last statement is the thing we want to prove.
Complementary angles add to 90 degrees. They form a right angle.
When "definition of congruence" is mentioned, we go from two angles being congruent to having them be of the same measure. It's a slight change of notation.
Vertical angles form whenever we cross two lines to form an X shape. The vertical angles are opposite one another, and always congruent.
The substitution property is the idea of replacing one thing with something it is equivalent to. In other words, we plug in the item.
Notice on line 2, if we replace "angle 1" with "angle 4" (valid because the two angles are congruent), and then replace "angle 2" with "angle 3", then we get the result on line 7.
Answer:
1. Given.
2. Definition of complementary angles.
3. Given.
4. Definition of congruent angles.
5. Vertical Angles Theorem.
6. Definition of congruent angles.
7. Substitution Property of Equality.
8. Definition of complementary angles.
Step-by-step explanation:
Statement 1
∠1 and ∠2 are complementary.
Reason: Given.
Statement 2
m∠1 + m∠2 = 90°
Reason: Definition of complementary angles.
Complementary angles are two angles that sum to 90°. Therefore, if ∠1 and ∠2 are complementary, then their measures must sum to 90°.
Statement 3
∠1 ≅ ∠4
Reason: Given.
Statement 4
m∠1 = m∠4
Reason: Definition of congruent angles.
Congruent angles are angles with exactly the same measure. As angle 1 is congruent to angle 4, then their measures are equal.
Statement 5
∠2 ≅ ∠3
Reason: Vertical Angles Theorem.
Vertical angles are always congruent.
Statement 6
m∠2 = m∠3
Reason: Definition of congruent angles.
Congruent angles are angles with exactly the same measure. As angle 2 is congruent to angle 3, then their measures are equal.
Statement 7
m∠4 + m∠3 = 90°
Reason: Substitution Property of Equality.
For all numbers a and b, if a=b, then a may be replaced by b in any equation or expression.
As m∠2 = m∠3 and m∠1 = m∠4, replacing them in m∠1 + m∠2 = 90° gives m∠4 + m∠3 = 90°.
Statement 1
∠3 and ∠4 are complementary.
Reason: Definition of complementary angles.
Complementary angles are two angles whose sum is 90°. Therefore, if the sum of m∠4 and m∠3 is 90°, this means that ∠4 and ∠3 must be complementary.
Which of the following traits do histograms, Pareto charts, and scatter plots have in common?
a) They are all bar charts.
b) They are all visual tools to display data.
c) They all show change over time.
d) All of the above.
Answers
The correct option is option (B) .
In other words Histograms , Pareto charts and scatter plots have a common thing that they are all visual tools to display data.
Histogram :
It show continuous data in ordered rectangular columns. There are usually no gaps between columns.
Histograms show the frequency distribution (shape) of a data set.To graphically summarize large datasets.Scatterplot :
A scatterplot is an x-y plot that shows the relationship between two variables. Used to plot data points on vertical and horizontal axes.
Predicts the behavior of the dependent variable based on the scale of the independent variable. If you just want to visualize the correlation between two large datasets without considering hours.Pareto Chart :
A Pareto chart is a common tool used by manufacturers to analyze quality and defect data, providing a quick visual representation of the frequency and cumulative percentage of occurrences of a particular problem.
A Pareto chart is a combination of a bar chart and a line chart.Hence , all of three have a common thing that is they visualize tools to represent the data
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Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H?
Answers
The coordinates of pre-image point H is (c) (3, 2)
How to determine the coordinates of pre-image point H?The graph represents the given parameter
On the graph, we have the coordinate of point H' (i.e. the image) to be
H' = (-3, -2)
The transformation rule is given as
Rotation 180° about the origin
Mathematically, this is represented as
(x, y) = (-x, -y)
This implies that:
H = (3, 2)
So, the coordinates are (3, 2)
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In math class 20% of the students did not finish their quiz. If 24 students finished their quiz, how many students are in math class?
Answers
Answer: 30 kids are in the math class
Step-by-step explanation: A simple way to solve this question is by knowing divisors. Since 24 is only 80% of X, then look for common divisors betweet 24 and 80% (4) If 6 is 20%, then 30 is 100%
How many seven-digit numbers can be formed with the digits of 2201213?
Answers
There are 420 arrangements for seven-digit numbers that can be formed with the digits of 2201213 by permutation.
What is permutation?The term permutation is simply the process of arrangement or selection of objects. It involves each of several possible ways in which a set or number of things can be ordered or arranged.
We can apply the formula for permutation;
[tex]p(n,r) = \frac{n!}{(n - r)!}[/tex]
where n = total number of object and r = number of objects selected.
Total number of digits = 7
number of the digit 2 = 3
number of the digit 1 = 2
number of the digit 0 = 1
number of the digit 3 = 1
so the permutation for the digits 2201213 is calculated as;
7!/(3! × 2! × 1! × 1!)
(7 × 6 × 5 × 4 × 3!)/(2 × 3!) {cancel out 3! with 3! and 4 with 2}
7 × 6 × 5 × 2
420 arrangements
Hence, by permutation, we can say that there are 420 arrangement for which seven-digit numbers can be formed with the digits of 2201213
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2x < 15
answer and how to solve please
Answers
Answer:
×= -7½
Step-by-step explanation:
2x<15
2x<15=0
2x= -15
x= -15/2
x= -7½
help with this question please!
Answers
Answer:
A. TPR
B. NM
C. 6
Step-by-step explanation:
1. The triangle NKM matches up with TPR. We also already knew KMN= PRT. So, it was just a matter of aligning the order.
2. If you flip PRT then TR will match with NM
3. 4x-3=21
4x-3+3=21+3
Simplify: 4x=24
4x/4=24/4
x=6