Answer:
179 billion liters
Step-by-step explanation:
The variable t represents years since 2000, so in the year 2000 the value of t is zero.
When t=0, the exponential term is 1, so the value of the function is the multiplier of the exponential factor, 179.
__
Approximately 179 billion liters of soda was consumed in 2000.
i am trying to find the horizontal distance between two towers. i don't understand how to put x=40/tan11.5 into the calculator and get the answer 196.6
By using trigonometric relations, we see that the horizontal distance is 196.6.
How to find the distance between the towers?
Remember the relation:
tan(a) = (opposite cathetus)/(adjacent cathetus).
In this case, the adjacent cathetus is the horizontal distance between the towers, the opposite cathetus is 40, and the angle is 11.5°.
Then we can write:
tan(11.5°) = 40/x
Solving for x:
x = 40/tan(11.5°)
This is the equation that you got, and it gives:
x = 40/tan(11.5°) = 196.6
Why you don't get this?
The problem may be that your calculator is in radians instead of degrees. It should say "DEG" instead of "RAD" if you want to evaluate trigonometric functions in degrees.
If you want to learn more about right triangles:
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1) write a system on equations with the solution (2, -3). Work the problem out using the substitution method
The system of the equations that have the solution of (2, -3) are given below.
3x + 2y = 0 and 3y = 2x - 13
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
Write a system of equations with the solution (2, -3).
From a single point, an infinite number of lines pass through this point.
Let one line is passing through the origin. Then the equation of the line will be
[tex]\rm y = \dfrac{-3}{2} (x)\\\\y = -1.5x[/tex]
And the other line is perpendicular to the line which is passing through the origin and a point (2, -3).
[tex]\rm y = \dfrac{2}{3} x + c[/tex]
Then this line also passes through a point (2, -3). Then the value of c will be
[tex]\rm -3 = \dfrac{2}{3} \times 2 + c\\\\c \ \ = -13[/tex]
Then the equation of the line will be
3y = 2x -13
More about the linear system link is given below.
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If you roll two fair six -sided dice, what is the probability that the sum is 5 or lower?
Answer:
The probability that the sum is 5 or lower for each dice when rolled is 25/36, since all numbers equal to or below 5 count. Since there are 5 numbers out 6 possible, 5/6 is the probability fo rolling 5 or lower for one. Multiply 5/6 by itself, since we are rolling twice 5/6 * 5/6 = 25/36 or about a 69.5% chance
Step-by-step explanation:
Answer:
5/18
Step-by-step explanation:
Khan Academy
[tex]cos(21) = \frac{4}{x} [/tex]
Please help! brainliest to first correct answer!
Change the subject of the formula L = v 4kt - p to k.
Answer:
[tex]\boxed{k = \frac{L^2 + p}{4t}}[/tex]
General Formulas and Concepts:
Algebra I
Basic Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle L = \sqrt{4kt - p}[/tex]
Step 2: Solve for k
We can use equality properties to help us rewrite the equation to get k as our subject:
Let's first square both sides:
[tex]\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\\end{aligned}[/tex]
Next, add p to both sides:
[tex]\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\& \rightarrow L^2 + p = 4kt \\\end{aligned}[/tex]
Next, divide 4t by both sides:
[tex]\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\& \rightarrow L^2 + p = 4kt \\& \rightarrow \frac{L^2 + p}{4t} = k \\\end{aligned}[/tex]
We can rewrite the new equation by swapping sides to obtain our final expression:
[tex]\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow \boxed{k = \frac{L^2 + p}{4t}}\end{aligned}[/tex]
∴ we have changed the subject of the formula.
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Topic: Algebra I
help me solve this algebra equation
Answer:
Perimeter = [tex]16\sqrt{5}[/tex]
Area = [tex]80[/tex]
Step-by-step explanation:
To find the perimeter of the square, you can use the square perimeter formula, [tex]P=4a[/tex], where [tex]a[/tex] is equal to the length of one side:
[tex]P=4a[/tex]
[tex]P=4(4\sqrt{5})[/tex]
[tex]P=16\sqrt{5}[/tex]
Then, to find the area of the square, you can use the square area formula, [tex]A=a^2[/tex], where [tex]a[/tex] is equal to the length of one side:
[tex]A=a^2[/tex]
[tex]A=(4\sqrt{5})^2[/tex]
[tex]A=80[/tex]
Therefore, the perimeter of the square is [tex]16\sqrt{5}[/tex] millimeters and the area of the square is [tex]80[/tex] square millimeters.
I hope this helps!
A random sample of 102 students found that 4 out of 6 students brought a lunch to school instead of eating the cafeteria food.
At this rate, how many students would eat the cafeteria food if 510 students were in attendance?
____ students
The random sample is that where every result (student for the case) has the same probability to be selected.
Then you cannot use any method that select one student with preference.
Two possible valid methods are:
- Write the number of each student in separate papers, put all the papers in a closed box and blind choose 102 papers.
- Assign a number to each student of the school and use a method to generate 102 random numbers.
Need help, don't know this
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=\stackrel{KL}{2}\\ \theta =\stackrel{\widehat{LM}}{\frac{14\pi }{9}} \end{cases}\implies A=\cfrac{ ~~ \left( \frac{14\pi }{9} \right)(2)^2 ~~ }{2}\implies A=\cfrac{28\pi }{9}[/tex]
4) Jonathan works at Subway and earns $10.00 an hour. He gets paid time and a half for every hour over 40, and is paid every 2 weeks. If he worked 43 hours the first week and 49 hours the second week, what is his gross pay? Regular hours- Regular wage- Regular Pay- Overtime hours- Overtime wage- Overtime Pay- Gross Pay-
Answer:
$980
Step-by-step explanation:
Regular hours- 40 per week
Regular wage- $10/hour
Regular Pay- (40 hours + 40 hours) × $10.00/hour = $800
First week: 43 hours = 40 hours regular + 3 hours overtime
Second week: 49 hours = 40 hours regular + 9 hours overtime
Overtime hours- 3 hours + 9 hours = 12 hours
Overtime wage- $10/hour × 1.5 = $15/hour
Overtime Pay- 12 hours × $15/hour = $180
Gross Pay- $800 + $180 = $980
A parallelogram has an area of 150 square yards and a height of 5 yards.
what is the length of the base of the parallelogram?
enter your answer in the box. a parallelogram has an area of 150 square yards and a height of 5 yards.
what is the length of the base of the parallelogram?
enter your answer in the box.
The length of the base of the parallelogram that has a height of 5 yards and an area of 150 square yards is 30 yards
How to determine the base length?The given parameters are:
Area = 150
Height = 5
The area of a parallelogram is:
Area = Base * Height
So, we have:
Base * 5 = 150
Divide both sides by 5
Base = 30
Hence, the length of the base of the parallelogram is 30 yards
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a map has a scale of 2cm to 5km
rewrite the scale as a ratio in its simplest form.
Answer:
1: 250 000
( There are 1000 metres in a km and 100 cm in a m, thus you multiply 5 km by 100 000 to convert it to cm, then you divide by 2 in order to get the simplist form of the ratio )
what is the best estimate
Answer:
D. 8.5
Step-by-step explanation:
The full value of √8 is 8.48528137...
Hope this helped!
help me with area please
Answer:
1-30ft (half circle) /60ft (full circle)
2-22in (half circle) 44in (full circle)
3-19yd (half circle) 38yd (full circle)
4-12yd (half circle) 24 yd (full circle)
5-6in (half circle) 12 in (full circle)
6 34ft (half circle) 58 (full circle)
Give brainliest :)
What is 5.2% of 6 x 10^8
Answer:
31200000
Step-by-step explanation:
Jeez who gave you this question?
Which is the equation of a parabola with a directrix at y=2 and a focus at (5,0)
Check the picture below, so the parabola looks more or less like so.
the vertex is always half-way between the focus point and the directrix, and since the parabola is opening downwards, the "p" distance is negative.
[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=5\\ k=1\\ p=-1 \end{cases}\implies 4(-1)(y-1)~~ = ~~(x-5)^2\implies -4(y-1)=(x-5)^2 \\\\\\ y-1=-\cfrac{1}{4}(x-5)^2\implies y=-\cfrac{1}{4}(x-5)^2 + 1[/tex]
help i dont have any check answer anymore
Answer:
10 maybe
Step-by-step explanation:
Which number set correctly represents the range of the given data? {(0, 0), (2, 0), (3, 0), (5, 0)} {0, 2, 3, 5} {0, 2, 3} {0, 2} {0}
{0}
Step-by-step explanation:The range of a function is the set of y-values within a function.
Finding the Range
As stated above, the range is all of the y-values. To find the y-values remember that in a coordinate pair the second point is the y-value. So, look at the second value of each pair. For all 4 points, the y-value is 0. This means that the range is 0.
Range Notation
Now that we know the range, we need to use the correct notation. When writing domain or range, make sure that the values are listed in order from least to greatest. Additionally, even if y-values repeat in the coordinate pairs, only state them once in the range. In this case, there is only 1 unique value, so the range should only have 1 value. Finally, the range is surrounded by braces. Therefore, the range should be written as {0}.
HELPP is please it’s math
Answer:
If the two side planks are equal lengths then the answer is 26 1/3.
the diagram shows a regular dodecagon
work out the size of one interior angle
the diagram shows a regular dodecagon is the size of one interior angle
find average of the numbers 8 , 13 , 15.
Answer:
12
Step-by-step explanation:
SUM/COUNT = formula
8+13+15/3
36/3
= 12
Evaluate arcsin(1) and arctan√3
The value of arcsin(1) is 90° and the value of arctan√3 is 60°
Evaluating trigonometric functionsFrom the question, we are to determine the values of arcsin(1) and arctan√3. That is, sin⁻¹ (1) and tan⁻¹(√3)
NOTE:
If sin x° = y, then sin⁻¹ y = x°
If cos x° = y, then cos⁻¹ y = x°
If tan x° = y, then tan⁻¹ y = x°
From the trigonometry table of values, we have that
sin 90° = 1
∴ sin⁻¹ (1) = 90°
arcsin(1) = 90°
Alos, from the trigonometry table of values, we have that
tan 60° = √3
∴ tan⁻¹(√3) = 60°
arctan√3 = 60°
Hence, the value of arcsin(1) is 90° and the value of arctan√3 is 60°
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Us mathematical symbols to write an inequality that compares -2 and -9
Answer:
-2 > -9
or
-9 < -2
Step-by-step explanation:
-2 > -9
Step-by-step explanation:Inequalities represent values by comparing their size to other numbers.
Negative Numbers
While positive 9 might be larger than positive 2, remember that negative numbers work in the opposite way. -9 is more negative than -2, thus it is smaller. Another way to think about it is that -9 is further below 0 than -2.
Inequality Symbols
There are 2 main inequality symbol < (less than) and > (greater than). The symbol opens to the side of the larger number. Because we know that -2 is greater than -9, we can make the inequality -2 > -9.
What is the probability that a die will land on the number 5? Answer as a fraction only!
Answer:
[tex]P(5)=\frac{1}{6}[/tex]
Step-by-step explanation:
Since the number 5 appears once on a 6-sided die, then [tex]P(5)=\frac{1}{6}[/tex]
Part
The boat rental company gave a roaring team a discount of $10 oft for every
4 days of rental The team rented a boat for 12 days. Their couch paid 35%
of the total discounted rental cost. The remaining rental cost was divided
equally among the 15 team members
• Determine the total cost for the team to rent a boat.
• Determine the cost per team member.
Enter your answers and your work or explanation in the space provided
Math symbols
$10
Relations
Gearrety
Answer:
i really dont know, i need help with it too
Step-by-step explanation:
Which of the following lines are shown in the drawing?
LI
GJ
CJ
BE
FA
WILL MARK BRAINLIEST
Answer:
FA Is the closest so thats your answer.
Step-by-step explanation:
please help help help meee
Answer:
Kaylaa do you use desmos graphing calculator? it's an online graphsing tool and would make this very easy for you. Maybe you are not allowed to use a calculator?
Step-by-step explanation:
with out a calculator it's a long math process, 1st because each of the equations are equal to Y, we can set each of them equal to each other. like this
[tex]\sqrt{x-8}[/tex] + 3 = - [tex](x-5)^{2}[/tex] + 18
[tex]\sqrt{x-8}[/tex] = - [tex](x-5)^{2}[/tex] +18 -3
[tex]\sqrt{x-8}[/tex] = - [tex](x-5)^{2}[/tex] + 15
[tex]\sqrt{x-8}[/tex] = -[ (x-5)*(x-5) ] + 15
[tex]\sqrt{x-8}[/tex] = -[ [tex]x^{2}[/tex] - 10x + 25] +15
[tex]\sqrt{x-8}[/tex] = -[tex]x^{2}[/tex] + 10x -25 +15
[tex]\sqrt{x-8}[/tex] = -[tex]x^{2}[/tex] + 10x -10
- [tex]\sqrt{x-8}[/tex] = [tex]x^{2}[/tex] - 10x +10
(- [tex]\sqrt{x-8}[/tex])^2 = ( [tex]x^{2}[/tex]- 10x +10)^2
this turns into a 4 order polynomial. I used a solver to find x
x = 8.75884.... approx
so the question asks what is the point at the nearest 1000th, which is 8.759
then they ask what is the point at the nearest 100th, which is
8.76
I'm attaching the graph, if it helps :P
What is the value expression -255 + (-15)?
A) -25
B) -15
C) 15
D) 25
Answer:
first we all know that minus multiply by minus will give you plus so,
-255-15=-270
Can someone help me please?!!
Reason:
Plug in w = 16 and compute.
D = 4w + 30
D = 4(16) + 30
D = 64 + 30
D = 94
This says at week 16, Jose will have $94 in his piggy bank.
can anyone help me determine if the figure is a trapezoid and why? anyone who answers will get a thanks and 5 stars of course (and brainly). any help appreciated
Find the volume of the prism where B is the base area.
Answer:
V = 58.14 ft²
Step-by-step explanation:
the volume (V) of the prism is calculated as
V = Bh ( h is the perpendicular height )
here B = 11.4 and h = 5.1 , then
V = 11.4 × 5.1 = 58.14 ft²
Answer:
V = 58.14 ft³
Step-by-step explanation:
V = B × h
= 11.4×5.1
= 58.14 ft³