Answer:
9
Step-by-step explanation:
5,6,7,8,9
An architect built a scale modelof a sports stadium using a scale in which 2 inches represents 30 feet.The height of the sport stadium is 180 feet.What is the height of the scale model in inches?
The scale model of the sports arena has a height of 12 inches.
What does unit rate mean?Unit rate is the amount of something at a rate of one amount to another amount.
If 2 inches = 30 feet, then a sports stadium's height is 180 feet.
A man can walk 6 kilometers in 2 hours.
A man can cover 3 miles by walking in an hour.
A machine can cut 10 potatoes in five minutes.
A machine can cut two potatoes in a minute.
30 feet equals 2 inches.
Add 30 to both sides.
1 foot equals 2/30 inches.
1 foot equals 2/30 inches today.
Add 180 to both sides.
180 feet equals 180 x 2/30 inches.
6 × 2 inches times 180 feet.
12 inches equal 180 feet
Since the height of the sports stadium is 180 feet, 2 inches would equal 30 feet.
The scale model of the sports arena has a height of 12 inches.
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C
18. Andrew works at Grub Burger and earns
$8.00 an hour. Create a graph of the
relationship between x, the number of hours
and y, the total amount Andrew earns. Then
write an equation to represent the relationship.
EARNINGS ($)
50
45
40
30
25
20
15
10
5
1 2 3 4 5 6 7 8 9 10
HOURS
The graph of the relationship between x, the number of hours, and y, the total amount Andrew earns attached below, and the equation represent the relationship y = 8x.
What is the graph of the equation?
The graph of an equation is the group of all points on a number line or the coordinate plane that are solutions of an equation (= statement that two amounts are equal).
0 hours- $0
4 hours- $32
8 hours- $64
12 hours- $96
First find the equation of this problem to represent the relationship, which is y = 8x.
Next, you substitute the number of hours into x to get y, which is the amount of money.
Hence, the graph of the relationship between x, the number of hours, and y, the total amount Andrew earns attached below, and the equation represent the relationship y = 8x.
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1.) ΔECD ≅ ΔECX
CD=?
By the congruence property CD ≅ CX
Congruent examples include what?
Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
Which five types of congruence are there?
If two triangles meet all 5 requirements for congruence, then they are congruent. They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) (RHS).
Given that:
ΔECD ≅ ΔECX
so ED ≅ EX
CD ≅ CX
by the congruence property
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Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x)=(x²-64)^{1/11} on the domain [-8,9]
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The absolute maximum is , which occurs at x= (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.)
B. There is no absolute maximum.
The critical points for the equation [tex]f(x)=(x^{2} +64)^{\frac{1}{11} }[/tex] is
[tex](x,f(x))[/tex] = [tex](0,2^{\frac{6}{11} })[/tex] = [tex](0,1.46)[/tex]. at x=0
The absolute maximum is at [tex](x,f(x))\\[/tex] = [tex](9,\sqrt[11]{145} )[/tex] = [tex](9,1.6)[/tex], at x=9.
What is the absolute maximum of an equation?
The highest conceivable values for f are represented by the absolute maximum (sometimes called the global maximum) of a function f(x) (x). Let's imagine the function's critical value, x=c, is present within its domain. If the inequality f(c) [tex]\geq[/tex] f(x), x is a domain, then the function f(x) is said to satisfy an absolute maximum when x=c.
To find the critical points, we find the value of f'(x) and equate to 0.
[tex]\frac{d}{dx} (\sqrt[11]{x^{2}+64} )=0[/tex]
we get x=0.
We see that f'(x) exists for all x between [-8,9].
We also find the endpoints, that is -8 and 9.
Then we calculate f(x) at critical points and endpoints.
We calculate f(x) at 0, -8, and 9.
We get,
for x=0, f(x)= [tex]2^{\frac{6}{11} }[/tex]
for x=-8, f(x)= [tex]2^{\frac{7}{11} }[/tex]
for x=9, f(x)= [tex]\sqrt[11]{145}[/tex]
We see that the value is maximum at x=9, and f(x) becomes [tex]\sqrt[11]{145}[/tex].
Hence we get the absolute maximum is [tex](x,f(x))\\[/tex] = [tex](9,\sqrt[11]{145} )[/tex] = [tex](9,1.6)[/tex]
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9. Delia bought $45 dollars worth of clothes, but the total including sales tax came to $54. What is
the sales tax rate that Delia paid?
of the vehicles
Answer:
20%
Step-by-step explanation:
You want to know the tax rate if the added tax brings the cost of $45 purchase to a total of $54.
MultiplierThe multiplier applied to a purchase cost to add the tax is ...
(1 +r)
where r is the tax rate.
Here, that means ...
45(1 +r) = 54
1 +r = 54/45 = 1.20
r = 1.20 -1 = 0.20 = 20%
The tax rate Delia paid on the articles she bought was 20%.
Given: C is the midpoint of DA and FE bisects LAED. List three congruence statements and reasons based on
the given information.
Triangles ΔAEC, ΔECD are congruent.
What are conditions of Congruency?Three angles and three sides, or the six measuring components, specify the requirements for the congruence of triangles. But if three of these are correctly satisfied, the other three are also satisfied automatically. Axioms for congruency are four such instances.
Triangles are said to be congruent if:
Congruent triangles under the SSS (Side Side Side postulate) condition.
Congruent triangles criterion according to the SAS (Side Angle Side postulate).
Congruent triangles are a requirement of the ASA (Angle Side Angle postulate).
The congruent triangles criterion of the AAS (Angle Angle Side postulate).
Given C is mid point of AD.
and, FE bisects the angle ∠AED.
By SAS Postulate we can say ΔAEC, ΔECD are congruent.
In triangles ΔAEC, ΔECD;
AC=CD (C is mid point)(S);
∠CEA=∠CED (Bisector)(A)
CE=CE (Common side)(S);
So by SAS theorem both are Congruent.
Triangles ΔAEC, ΔECD are congruent.
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The table represents some points on the graph of a linear function.
Which equation represents the same relationship?
x-2y-1=0
2x-y +7=0
y+3= 1/2 (x - 5)
y-15 = 2(x-31)
The equation that represents the same relationship is equation 1: x-2y-1=0
How to find the equation?We should know that an equation is a mathematical statement that shows the equality of two sides o a statement.
From the given equation:
x-2y-1=0
If we input the various values of x such as -5, 7,31,42 into the equation we are going to obtain the corresponding values of y as indicated in the table
x-2y-1=0
Rewrite the equation
x-1=2y
⇒2y=x-1
=2y=-5-1
y=-3
Also, 2y=7-1
2y=6
y=3
Input the value 31 into the equation or x
2y=31-1
2y=30
y=15
Input the value 45 or x in the equation
2y=45-1
2y=44
y=22
In conclusion, the equation x-2y-1=0 represents the the same relationship in the table
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Solving distance, rate time problem
A total of 396 miles and 2.2 hours will pass between the two trains on the Long.
How to calculated the Distance and rate time?For additional information on how to handle rate-time-distance or motion problems, scroll down the page.
Moving away from one another are the two trains.
85x + 95x = 396
To solve you combine like terms. The like terms are 85x and 95x
85x + 95x = 180x
Right now, you
180x = 396
Now multiply by 180.
180 divided by 396 equals 2.2.
X= 2.2
That's how you do things, in my opinion.
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If A and B are independent events with P(A)=0.5 and P(B)=0.1, find P(A AND B).
The probability of event A and event B of the independent events will be 0.05.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the conditional probability is given as,
P(A and B) = P(A) x P(B)
Event A and event B are independent events. The probability of event A is 0.50 and the probability of event B is 0.10.
Then the probability of event A and event B of the independent events is given as,
P(A and B) = P(A) x P(B)
P(A and B) = 0.50 x 0.10
P(A and B) = 0.05
The probability of event A and event B of the independent events will be 0.05.
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can someone help me with this thank you
Step-by-step explanation:
we know that the two angles with x are equal since they are made with the same lines
so
8x+36=5x+51
solve for x
a. subtract 36 from both sides
8x=5x+15
b. subtract 5x on both sides
3x=15
c. divide by 3
x=3
now to find z
we know a line equals 180
so
(8x+36)+z=180
plug in 3
8(3)+36+z=180
24+36+z=180
60+z=180
z=120
A triangle has side lengths of 200 units and 300 units. Write a compound inequality for the range of the possible lengths for the third side,
Answer:
100<x<500
Step-by-step explanation:
We can create a system of inequalities by using the Triangle Inequality Theorem. This theorem states that the sum of two sides on a triangle is greater than the other sides.
1.) Figure out the first inequality. This would be 300+200>x, or x<500.
2.) Figure out the second inequality. This would be x + 200 > 300, or x>100.
3.) Figure out the third inequality. This would be x + 300 > 200, or x > -100.
4.) Combine these inequalities. By combining these inequalities, we would get 100<x<500.
What is the equation in slope-intercept form of the line that passes through the points (6,1) and (3,3)?
y=−2/3x+5y
y=−2/3x−10y
y=2/3x+2y
y=2/3x−2
The equation in slope intercept form of the line that passes through the points (6,1) and (3,3) is y = - 2 / 3 x +5
How to find equation in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation in slope-intercept form of the line that passes through the points (6,1) and (3,3) can be represented as follows;
let's find the slope
m = 3 - 1 / 3 - 6
m = - 2 / 3
Hence, let's find the y-intercept as follows;
using (3, 3)
y = - 2 / 3 (x) + b
3 = - 2 / 3 (3) + b
3 + 2 = b
b = 5
Therefore, the equation of the line is y = - 2 / 3 x +5
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Morris Company applies overhead based on direct labor costs. For the current year, Morris Company estimated total overhead costs to be $408,000, and direct labor costs to be $2,040,000. Actual overhead costs for the year totaled $386,000, and actual direct labor costs totaled $1,820,000. At year-end, Factory Overhead is:
At year-end, Factory Overhead is debit of $34000.
What is profit and loss?
A profit and loss (P&L) statement could be a monetary report that has a outline of a company’s revenue, expenses and profit. It provides investors and alternative interested parties an insight into however an organization is working and whether or not it's the flexibility to get a profit.
Main Body:
Estimated total overhead costs = $456,000
Estimated direct labor costs = $2,280,000
Actual overhead costs= $422,000
Actual direct labor costs= $1,940,000
To calculate the factory overhead, we need to first calculate Estimated overhead rate.
Estimated overhead rate = Estimated total overhead costs / Estimated direct labor costs
= $456,000 / $2,280,000
= 0.2
= 20%
Therefore;
Actual Factory overhead = Actual direct labor cost × application rate
= $1,940,000 × 20%
= $388,000
We can get the balance in the overhead account as shown below;
Balance = Actual overhead cost - Actual cost that should be applied
= $422,000 - $388,000
= $34,000 (Debit).
Hence there is debit of $34000.
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you have a bag of ping pong balls. you arrange all but 2 of the balls in an equilateral triangle. then you put all the balls back into the bag and create a new equilateral triangle where each side has one more ball than the first arrangement but this time you are 11 balls short. how many balls were in the first arrangement?
Answer:
The “edge” effect of a tetrahedral container with edge length of 1,000 mm would be 2*r*√3 (r = radius of ball, see diagram below). For a ping pong ball with a diameter of 40 mm, the edge effect would be 2*20*√3 = 69.28 mm. Subtract that from 1,000 mm and you get 930.72 mm of “available space” along the bottom row. Divide 930.72 mm by 40 mm per ball and you get 23.27. So you wouldn’t be able to fit 24 balls along the base, you’d only be able to fit 23 balls. With 23 balls, the total number that a tetrahedron could contain (T) would be T = n(n+1)(n+2)/6 = 2,300 balls, not 2,600.
Given dy/dt=2y and y(2)=200. Find y(7).
The required value of y(7) is given as y (7)= 4412711.8.
Given that,
Given dy/dt=2y and y(2)=200.
The action of bringing concurrently shorter components into a single system that acts as one is known as integration.
Here,
dy/dt = 2y
dy/y = 2dt
integrate,
logy = 2t + c
[tex]y = e^{2t + c}[/tex]
put t = 2 and y = 200
C = 1.3
Now,
[tex]y= e^[2t + 1.3][/tex]
Substitute t = 7
[tex]y= e^[14 + 1.3]\\y = e^{15.3}[/tex]
y = 4412711.8
Thus, the required value of y(7) is given as y (7)= 4412711.8.
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I need help
Arc QR =
Arc RS=
QPS =
PSR =
SRQ =
Applying the inscribed angle theorem, the measures of the angles and arcs in the image given are:
Arc QR = 48°
Arc RS = 96°
Arc QPS = 216°
Arc PSR = 186°
Arc SRQ = 144°
What is the Inscribed Angle Theorem?The inscribed angle theorem state that the measure of an intercepted arc is equal to twice the measure of the inscribed angle.
Find arc PSR:
Arc PSR = 2(93) [based on the inscribed angle theorem]
Arc PSR = 186°
Find arc QR:
Arc QR = 360 - arc PQ - arc PSR
Substitute
Arc QR = 360 - 126 - 186
Arc QR = 48°
Arc RS = arc PSR - arc PS
Arc RS = 186 - 90
Arc RS = 96°
Arc QPS = 126 + 90
Arc QPS = 216°
Arc PSR = arc PS + arc RS
Arc PSR = 90 + 96
Arc PSR = 186°
Arc SRQ = arc RS + arc QR
Arc SRQ = 96 + 48
Arc SRQ = 144°
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Answer: 48 96
Step-by-step explanation:
Arc QR = 360 - 126 - 186
Arc QR = 48°
Arc RS = arc PSR - arc PS
Arc RS = 186 - 90
Arc RS = 96°
to serve one person at a local restaurant it takes 10 minutes to serve pot five people it takes 18 minutes right and solve an equation to find the number of minutes it will take to serve a party of eight
By finding an evaluating a linear equation we will see that it takes 24 minutes to serve a group of 8 people.
How long takes to serve a party of eight?
Let's assume that the relation between the number of people and the time it takes to serve them is linear.
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
a = (y2 - y1)/(x2 - x1)
Here we have two points:
1 person, 10 minutes, written as (1, 10)
5 people, 18 minutes, written as (5, 18)
Then the slope is:
a = (18 - 10)/(5 - 1)
a = 8/4 = 2
Then the linear equation is:
y = 2x + b
To find the value of b, we can replace the values of one of the points, I will use (1, 10) so we will get:
10 = 2*1 +b
10 = 2 + b
10 - 2 = b
8 = b
The linear equation is:
y = 2x + 8
For 8 customers, the time will be:
y = 2*8 + 8
y = 24
It will take 24 minutes to serve 8 people.
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Zeno jumped 8 meters. Then he jumped half as far again (4 meters). Then he jumped half as far again ( 2 meters). So after 3 jumps, he was 8+4+2=14 meters from his starting place.
a) Zeno kept jumping half as far again. How far would he be after 4 jumps? 5 jumps? 6 jumps?
b) Before he started jumping, Zeno put a mark on the floor that was exactly 16 meters from his starting place. How close can Zeno get to the mark if he keeps jumping half as far again?
a) His distances after each jump are given as follows:
4 jumps: 15 meters.5 jumps: 15.5 meters.6 jumps: 15.75 meters.b) He will jump exactly 16 meters.
What is a geometric sequence?In a geometric sequence, each term is obtained by the multiplication of the previous term by the common ratio.
In this problem, the sequence is given as follows:
8, 4, 2, ...
The common ratio is of:
q = 2/4 = 4/8 = 0.5.
Then the next jumps are given as follows:
4th jump: 2 x 0.5 = 1 meter -> 14 + 1 = 15.5th jump: 2 x 1 = 0.5 meters -> 15 + 0.5 = 15.5.6th jump: 2 x 05 = 0.25 meters -> 15.5 + 0.25 = 15.75.The sum of the elements of an infinite geometric sequence is given as follows:
[tex]S = \frac{a_1}{1 - q}[/tex]
In which [tex]a_1[/tex] is the first element.
Hence for this problem, the sum is of:
S = 8/(1 - 0.5) = 16 meters.
Which means that he will reach exactly the desired distance.
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Phoebe had $14.27. Then she earned $8.75 for raking her neighbor's leaves.
How much money does she have now?
Answer:
$23.02
Step-by-step explanation:
You add what she earned to what she had before
$14.27 + $8.75 = $23.02
A lioness has 4 cubs that weigh 1.7 kg, 2.1 kg, 3 kg, and 2.7 kg. Each cub eats 1.25 kg of food a day. How much food will be needed to feed all the cubs for one year?
The quantity of food that would be needed to feed all the cubs for one year is 1825 kg
Calculating the quantity of food that would be needed to feed cubsFrom the question, we are to determine how much food would be needed to feed all the cubs for one year
From the given information,
"Each cub eats 1.25 kg of food a day"
Assume there are 365 days in a year.
Since there are 4 cubs,
The quantity of food that would feed the cubs for one year = 365 × 4 × 1.25
The quantity of food that would feed the cubs for one year = 1825 kg
Hence, the quantity of food needed is 1825 kg
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There were 202 tickets sold during the first hour of sales for the opening match of the
World Cup. Tickets for the cheap seats cost $50, and the best seats cost $556. Use algebra
to find out how many tickets of each type were sold if the total receipt was $42,990,
Answer:
137 cheap tickets sold, and 65 best seats sold
Step-by-step explanation:
x+y=202
50x+556y=42900
x=202-y
50(202-y)+556y=42900
10100-50y+556y=42900
10100+506y=42900
506y=32890
y=65
x=202-65
x=137
x= Cheap tickets, y= expensive tickets
The number line includes points A, B, C and D which statement is true.
Answer:
yes youre right it is point D
Step-by-step explanation:
any help on this question
Using law of logarithm and exponent rules, the value of the unknown is 5
Logarithmlogarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation. For example, if 102 = 100 then log10 100 = 2.
Logₐ x = n or aⁿ = x
Where b is the base of the logarithmic function.
This can be read as “Logarithm of x to the base b is equal to n”.
In this case, we just need to solve for the value of b
4 = logₐ(625)
4 = 1 / log625(a)
multiply both sides by log₆₂₅(x)
log₆₂₅(a) / 4 = 1/4
applying log rules
a = 5
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4 divide 5/6 as a mixed number ??
Answer: exact form is 24/5, decimal form is 4.8 and mixed number form is 4 4/5
Step-by-step explanation:
Answer:
4 4/5 (simplified)
Step-by-step explanation:
Using reciprocals:
4 divided by 5/6 = 4 x 6/5
= 24/5 = 4 4/5
To check: 4 4/5 x 5/6 = 4
You can use the same method for similar problems
what is the importance of knowing the history of the earth
Knowing the history of the Earth is of the utmost importance to understand how it got to now and to know where we are going.
¿What is the history of the Earth?The history of the Earth is nothing more than the set of events, occurrences and phenomena that the same happened from its origin to the present.
Knowing the history of the Earth is very important because:
It gives us knowledge about the development of the Earth and different associated elements.It allows us to understand different elements of the universe. It allows us to study and analyze different events associated with man and life.¡Hope this helped!
Answer:
The history of the Earth is nothing more than the set of events, occurrences and phenomena that the same happened from its origin to the present.
TEXT ANSWER
An airplane has stopped to refuel. Fuel is being added to the plane's gas tank at a constant
rate. After 13 minutes, there are 32,882 gallons of fuel in the plane; after 31 minutes, there
are 34,902.5 gallons in the plane. Write the y = mx + b equation that describes this
scenario.
W
You can refer to time 31:05 in the video above for a solution to a very similar example.
Please show your work below.
H
Normal
Enter your answer here
√x
E BIUS X₁ X²
22 Ix
Practice.
A JA
The function in f(t) form that describes the amount of fuel in the plane at time t will be:
f(t) = 112.25t + 31.425.75
What is the Equation of line?
The equation of the line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
we have given that;
After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.
Now,
Since, After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.
Hence, The equation of line passes through the points (13, 32882) and (31, 34902.5)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (32882 - 34902.5) / ((31 - 13)
m = 2020.5 / 18
m = 112.25
Thus, The equation of the line with slope 112.25 is,
⇒ y - 32885 = 112.25 (x - 13)
⇒ y - 32885 = 112.25x - 1459.25
⇒ y = 112.25x - 1459.25 + 32885
⇒ y = 112.25x + 31.425.75
Therefore, The function in f(t) form that describes the amount of fuel in the plane at time t will be:
f(t) = 112.25t + 31.425.75
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The figures shown below are similar and the labeled sides are corresponding.
If the perimeter (P₂) of figure 2 is 25 ft then what is perimeter (P₂) of figure 1?
P1=feet
The Perimeter of the Pentagon in Figure 1 is 40ft
What is Pentagon?
A pentagon is a two-dimensional polygon having five sides and five angles. "Penta" means "five," and "gon" means "angles" in Greek, therefore when we mix the two words "penta + gon," we obtain the term "pentagon."
Solution:
Permieter of Pentagon = 5 * side
In Figure 1, the length of a side is 8 ft,
Then the Perimeter will be 8*5 = 40ft.
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there is a line that includes the point 9,7 and has a slope of 1. what is its equation in slope intercept form?
Step-by-step explanation:
Note that the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Plug in the slope for m and the given coordinate for x and y:
9 = (7)(2) + b
9 = 14 + b
b = -5
y = 7x - 5
Write the linear equation in slope-Intercept form that passes through the given points.
4. (1.3) and (-3,-5)
6. (-12, 14) and (6,-1)
5. (1, 4) and (6, -1)
Answer:
1.3,-12,16
Step-by-step explanation:
Kim ran a 26-mile marathon.
She ran 1/7 of the marathon during
the first hour. How many miles did
Kim run during the first hour?
Answer:3.71 miles
Step-by-step explanation: