Answer:
3000
Step-by-step explanation:
Tony will donates $3000 after 5 years.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Donated amount= $1000
Tony is able to donate 3/2 times the amount that Theresa donates.
let Theresa donates x dollar each year
So, x+ 3/2x = 1000
5x/2 = 1000
5x = 2000
x= 400
Thus, Tony donate = 3/2 x 400 = $600
Hence, After 5 years Tony will donate= 600 x 5= $3000
Learn more about Algebra here:
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A bucket has a leak that started 6 hours ago. At time 0, when the bucket just emptied, a tap was turned on for 3 hours. The amount of water in the bucket can be modeled by the function f(x) = |x| over the interval [−6, 3], where x is the time, in hours, and y is the amount of water in the bucket, in gallons. Which translation of the graph represents the last 3 hours of the leak, and the tap running for 6 hours? Group of answer choices g(x) = |x − 3| g(x) = |x| + 3 g(x) = |x| − 3 g(x) = |x + 3|
Answer:
The answer is g(x) = |x - 3|
Step-by-step explanation:
Here we have a general problem of horizontal translations, we will see that the correct option is g(x) = |x - 3|
We know that the bucket was leaking for 6 hours, and then it was filled in 3 hours.
Then in the interval [-6, 0) the bucket was leaking
In the interval [0, 3] the bucket was being filled.
Now we want a transformation that represents the last 3 hours of leaking.
Also, remember that for a general function f(x), an horizontal translation of N units is written as:
g(x) = f(x + N)
If N is positive, the translation is to the left
If N is negative, the translation is to the right.
If we want to represent the last 3 hours of leaking (which happen for negative values of x) then we need to move the whole graph to the right.
So, if we define the function as:
g(x) = f(x - 3)
when we evaluate g(x) in zero we get:
g(0) = f(-3)
So this new function, at the time zero, starts representing the last 3 hours of leaking of the bucket.
Remembering that f(x) = |x|
We can see that the correct option is:
g(x) = f(x - 3) = |x - 3|
g(x) = |x - 3|
Below you can see a graph with a comparison of f(x) and g(x), where the green one is f(x) and the blue one g(x).
If you want to learn more, you can read:
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Given the equation ay − b = c, which expression represents y? a.) c-b/a b.) c+b/y c.) c+b/a d.) c+a/b
Answer:
Option C. y = ( c + b ) / a
Step-by-step explanation:
For this problem, we must simply isolate the y variable from the unknowns a, b, and c.
ay - b = c
ay - b + b = c + b
ay = c + b
ay * ( 1 / a ) = ( c + b ) * ( 1 / a)
y = ( c + b ) * ( 1 / a )
y = ( c + b ) / a
Thus, we will want to choose option C.
Cheers.
Forty-two people charter a bus for $788. Estimate the amount each person pays.
Your answer
Answer:
$20
Step-by-step explanation:
If 42 people equally share the bus price off 788 dollars then ech person would be expected to pay 788/42 = $18.76 (2dp) though I suppose if you needed to estimate it, you would round 788 to 800 and 42 down to 40 which would give you 800/40 = 20 dollars per person which is a pretty close estimate.
Hope this helped!
What equation matches this situation?
—John wants to buy an MP3 Player that costs $30. How much change did he receive
if he gives the cashier $40–
CAN SOMEONE HELP AND EXPLAIN THIS TRIGONOMETRY PROBLEM
Step-by-step explanation:
Hey there!
Simply work with it.
As it is a Right angled triangle, taking angle 40° as a reference angle. Then,
Length of board = hypotenuse = 15 feet.
To find: height of ladder = perpendicular.
Now,
Taking sin ratio,
[tex] \sin = \frac{p}{h} [/tex]
[tex]sin \: 40 = \frac{p}{15} [/tex]
or, as in per the given sin value is 0.6428
so,
[tex]0.6428 = \frac{p}{15} [/tex]
or, 15 × 0.6428 = p
or, p = height of ladder = 9.642.
Therefore, p = height of ladder = 10 feet. { rounding off we get 10 feet as answer}.
Hope it helps...
The product of 2 and a number x is 3/4. What is the value of x? x=5/4 x=3/8 x=1 1/4 x=3/2
Answer:
x=3/8
Step-by-step explanation:
2*x=3/4
x=3/4*2
x=3/8
Answer:
9
Step-by-step explanation:
What is the distance rounded to the nearest tenth, between the points (0, 5) and (8, 0)?
Answer:
9.4
Step-by-step explanation:
The distance formula is d=√((x₂-x₁)²+(y₂-y₁)²)
d=√((8-0)²+(0-5)²)
d=√((8²)+(-5²))
d=√(64+25)
d=√(89)
d=9.433981
d=9.4
Hope this helps :-)
Answer: 9.4 units
Step-by-step explanation:
Which statement best illustrates using the vertical line test to determine if the graph below is a function of x?
The graph is not a function of x because the line x = 0 intersects the graph at two points.
The graph is a function of x because the line x = 5 does not intersect the graph.
The graph is not a function of x because the line y = 0 intersects the graph at two points.
The graph is a function of x because the line y = 5 does not intersect the graph.
Answer:
The answer is either a or c .
Step-by-step explanation:
Answer:
c yw
Step-by-step explanation:
Please help me with this answer
Answer:
0.703
Step-by-step explanation:
19/70 = 70.37/100
Hope This Helps :)
Answer:
0.7037
Step-by-step explanation:
0.7037 is a decimal and 70.37/100 or 70.37% is the percentage for 19/27.
What is the pattern as the exponents decrease
Answer:
Divide the previous value by 5
Step-by-step explanation:
2(c + 3) = c - 13
Solve
Answer:
-19
Step-by-step explanation:
2 (c + 3) = c - 13
2c + 6 = c - 13
2c + 19 = c
19 = - c
c = - 19
imagine an investigation in which 40 students were asked to determine their chronotype by choosing from among four chronotypes instead of three: morning person, night person, neither, or both. If there is no relationship between chronotype and birth month, about what fraction of the students would you expect to pick the chronotype that matches their birth month? why do you think this?
Step-by-step explanation:
A chronotype is a behavioral manifestation of an underlying circadian rhythms of the myriad physical processes.
The chronotype word may be defined as an individual's natural tendency to remain active mostly at certain times of the day. Some people remain active and alert in the early time of the day and some are alert and active in the late night.
The chronotypes are : Morning person, night person, neither/both.
It is assume that the birth month and year of a person influences his or her chronotype. But if birth month is not related to theses personality traits of a person, then it can be expected that nearly 1/3rd of the fraction of the students in class picks the chronotype which corresponds to their birth type.
2
3) In which quadrant of the coordinate plane will the ordered pair (-8, 7)
be found? *
Answer:
2 cuadrante
Step-by-step explanation:
A recipe that makes a dozen cookies calls for 1 1/2 cups of milk, 2.25 cups of flour, and 1 1/4 cups of other ingredients. How many cups of other ingredients, milk and flour are needed to make 36 cookies? (1 dozen is 12 cookies)
Answer:
15 cupsStep-by-step explanation:
[tex]1\frac{1}{2} \:cups \:of\:milk\\2.25\:cups \:of\:flour\\1\frac{1}{4} \:cups\:of\:other\:ingredients\\\\Total = 1\frac{1}{2} + 2.25 + 1\frac{1}{4} \\= 5\:cups\\\\1\:dozen = 5\:cups\\3 \:dozen(36\:cookies) = x \:cups\\\\Cross\:multiply\\\\x = 5\times 3\\x = 15 \:cups[/tex]
1) 9 + 2h - 16
-7 + 2h
You are building a shelf that fits in a corner in the figure the entire shelf is XYZ each unit in the coordinate plane represents one inch find the area a of the shelf X is (15,20) Z is (0,5) Y is (15,5)
Answer:
[tex]Area = 112.5[/tex]
Step-by-step explanation:
Given
[tex]X = (15,20)[/tex]
[tex]Y = (15,5)[/tex]
[tex]Z = (0,5)[/tex]
Required
Determine the area of the triangle
The area is calculated using the following formula:
[tex]Area = |\frac{X_x(Y_y - Z_y) + Y_x(X_y - Z_y) + Z_x(X_y - Y_y)}{2}|[/tex]
Where
[tex](X_x,X_y) = (15,20)[/tex]
[tex](Y_x,Y_y) = (15,5)[/tex]
[tex](Z_x,Z_y)= (0,5)[/tex]
Substitute right values in the given formula:
[tex]Area = |\frac{15(5 -5) + 15(20 - 5) + 0(20 - 5)}{2}|[/tex]
[tex]Area = |\frac{15(0) + 15(15) + 0(15)}{2}|[/tex]
[tex]Area = |\frac{0 + 225 + 0}{2}|[/tex]
[tex]Area = |\frac{225}{2}|[/tex]
[tex]Area = |112.5|[/tex]
[tex]Area = 112.5[/tex]
Hence, the area of the triangle is 112.5
It was 12°C one person got home from school. The weather for port show me a story moving in the world drop the temperature by 70 Celsius. What is the expected temperature?
Answer:
Expected temperature = - 58°C
Step-by-step explanation:
Given:
Current temperature = 12°C
Drop in temperature = 70°C
Find:
Expected temperature
Computation:
Expected temperature = Current temperature - Drop in temperature
Expected temperature = 12°C - 70°C
Expected temperature = - 58°C
Are terms and ratios related?
Which of the following is a quantitative variable?
Temperatures in New York from January to March
Price of gas at three different gas stations
Population density of a town
Symbols of elements on the periodic table
Answers: A, B, C
These three deal with numeric values, so that is why they are quantitative variables. Think quantitative as quantity to help remember.
In contrast, choice D is a qualitative variable. Instead of dealing with numbers, it deals with symbols or labels. You could also call this a categorical variable (each label being its own category).
solve this question please: x² = -169
Answer:
13i, -13i
Step-by-step explanation:
To solve this equation, we need to take the square root of both sides. The square root of 169 can be either 13 or -13, but this time, they asked for -169. Whenever we take the square root of a negative number, we put the letter i, which stands for imaginary. It is never capitalized, so we remove the negative sign from -169, and take the square root of that. We get -13 and 13 as our answers, and we multiply both numbers by i to get -13i and 13i. Any solutions with i in it are considered complex solutions
Find the slope of the line through each pair of points. (-17,-5), (15.-13)
I need help with solving this equation! ( answer is supposed to be 3.888 but I have been getting a different answer every time!) 3.24 x 1.2
Answer:
I got 3.888 because when 4×2=8 and 2×2=4 and 3×2=6 so for my first row of numbers was 648 under 0 I put a 0 then multiplied 3.24 by 1 then added 648+3240=3.888
Answer:
Step-by-step explanation:
If you can't use a calculator break it apart.
1 X 3.24 is 3.24
Now take .2 x 3.24 this is easy, just remember to move the decimal in the answer one more to the left.
3.24
x .2
.684 moved the decimal one more spot
Now we take 3.24 + .684
3.24
+ .648
3.888
can you please tell me the right ans
Answer: i) 512,000 cm³ ii) 512,000 cc iii) 512 litres
Step-by-step explanation:
Volume (V) of a cube is side (s) cubed: V = s³
Given: s = 80 cm
i) V = (80 cm)³
= 512,000 cm³
ii) 512,000 cm³ = 512,000 cc
iii) 512,000 cm³ × 1 liter/1000 cm³ = 512 liters
The point (1/3,1/4) lies on the terminal said of an angle. Find the exact value of the six trig functions and explain which functions are reciprocal functions to each other
Answer:
sine and cosec are inverse of each other.
cosine and sec are inverse of each other.
tan and cot are inverse of each other.
Step-by-step explanation:
Given point on terminal side of an angle ([tex]\frac{1}{3},\frac{1}4[/tex]).
Kindly refer to the attached image for the diagram of the given point.
Let it be point A([tex]\frac{1}{3},\frac{1}4[/tex])
Let O be the origin i.e. (0,0)
Point B will be ([tex]\frac{1}{3},0[/tex])
Now, let us consider the right angled triangle [tex]\triangle OBA[/tex]:
Sides:
[tex]Base, OB = \frac{1}{3}\\Perpendicular, AB = \frac{1}{4}[/tex]
Using Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow OA^{2} = OB^{2} + AB^{2}\\\Rightarrow OA^{2} = \frac{1}{3}^{2} + \frac{1}{4}^{2}\\\Rightarrow OA = \sqrt{\frac{1}{3}^{2} + \frac{1}{4}^{2}}\\\Rightarrow OA = \sqrt{\frac{4^2+3^2}{3^{2}.4^2 }}\\\Rightarrow OA = \frac{5}{12}[/tex]
[tex]sin \angle AOB = \dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\Rightarrow sin \angle AOB = \dfrac{\frac{1}{4}}{\frac{5}{12}}\\\Rightarrow sin \angle AOB = \dfrac{3}{5}[/tex]
[tex]cos\angle AOB = \dfrac{Base}{Hypotenuse}[/tex]
[tex]\Rightarrow cos \angle AOB = \dfrac{\frac{1}{3}}{\frac{5}{12}}\\\Rightarrow cos\angle AOB = \dfrac{4}{5}[/tex]
[tex]tan\angle AOB = \dfrac{Perpendicular}{Base}[/tex]
[tex]\Rightarrow tan\angle AOB = \dfrac{3}{4}[/tex]
[tex]cosec \angle AOB = \dfrac{Hypotenuse}{Perpendicular}[/tex]
[tex]\Rightarrow cosec\angle AOB = \dfrac{5}{3}[/tex]
[tex]sec\angle AOB = \dfrac{Hypotenuse}{Base}[/tex]
[tex]\Rightarrow sec\angle AOB = \dfrac{5}{4}[/tex]
[tex]cot\angle AOB = \dfrac{Base}{Perpendicular}[/tex]
[tex]\Rightarrow cot\angle AOB = \dfrac{4}{3}[/tex]
9 tickets cost $54. How much do 4 tickets cost?
Let's make a proportion to solve this problem.
[tex]\frac{9}{54}=\frac{4}{x}[/tex]
[tex]9x=216[/tex]
[tex]x=24[/tex]
4 tickets cost $24
Hope this helps.
頑張って!
Mike ans his three friends decided to divide the lunch bill evenly.They are trying to figure out how much each person owes if the total bill was $52. Which equation models the scenario? a)52/4=x b)52/3=x c)52x=4 d)52x=3
Answer:
b
Step-by-step explanation:
x is the number each person will get
b is the only possible answer
6y-10y-11=8y-2y+29 step by step?
Step-by-step explanation:
6y - 10y - 11 = 8y - 2y + 29
6y - 10y +16y - 11 = 8y - 2y + 29 + 16y
-11 = 22y + 29
11 = 22y + 40
-29 = 22y
Not sure yet I think I made a mistake hold up
Consider the following 8 numbers, where one labelled x is unknown. 42, 47, 5, x , 18, 12, 50, 1 Given that the range of the numbers is 59, work out 2 values of x .
===========================================================
Explanation:
Let's assume that x is the largest value of the list. If so then x = 60 because
range = max - min
range = x - 1
range = 60-1
range = 59
Effectively, you work backwards to go from a range of 59 to have x = 60 as the max.
So x = 60 is one possible value. We can't have x any larger or the range would be larger.
But we can have x be smaller. Specifically, it would be the min of the list. If negative x values are allowed, then x = -9 is the other possible x value
Here's why
range = max - min
range = 50 - x
range = 50 - (-9)
range = 50+9
range = 59
If ƒ(x) = 2x2 + 3, then which of the following represent ƒ(-1)?
Answer:
f(-1) = 1
Step-by-step explanation
[tex]f(-1)= 2(-1)^{2} + 3\\f(-1) = -2 + 3\\f(-1) = 1[/tex]
Given the equation, 5x + 10y = 20, what are your x and y-intercepts? Explain your thought process and steps in your reply.
Answers:
x intercept = 4
y intercept = 2
============================================
Explanation:
To find the x intercept, plug in y = 0 and solve for x
5x+10y = 20
5x+10(0) = 20
5x = 20
x = 20/5
x = 4
The x intercept is x = 4, which means it is located at the point (4,0)
-----------------------
We'll flip things around for the y intercept. Plug in x = 0 and solve for y to get the y intercept.
5x+10y = 20
5(0)+10y = 20
10y = 20
y = 20/10
y = 2
The y intercept is located at (0,2), but we can just say "the y intercept is 2" as an alternative.