Answer:
600mL
Step-by-step explanation:
1 Milliliter = 0.001 L
Determine the value of y in the inequality.
18 + 6y < 42
y < −7
y > −7
y < 4
y > 4
Answer:
y>-7
Step-by-step explanation:
Answer:
the answer is option 3
Step-by-step explanation:
18+6y<42
6y<42-18
6y<24
y<4
The population of a village is 6400. The population is decreasing exponentially at a rate of r% per year. After 22 years, the population will be 2607. Find the value of r.
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$2607\\ P=\textit{initial amount}\dotfill &6400\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\dotfill &22\\ \end{cases} \\\\\\ 2607=6400(1 - \frac{r}{100})^{22} \implies \cfrac{2607}{6400}=\left( \cfrac{100-r}{100} \right)^{22} \implies \sqrt[22]{\cfrac{2607}{6400}}=\cfrac{100-r}{100}[/tex]
[tex]\cfrac{r-100}{100}=-\sqrt[22]{\cfrac{2607}{6400}}\implies r-100=-100\sqrt[22]{\cfrac{2607}{6400}} \\\\\\ r=100-100\sqrt[22]{\cfrac{2607}{6400}}\implies {\Large \begin{array}{llll} r\approx 4 \end{array}}[/tex]
Ajay is working two summer jobs, making $8 per hour washing cars and $11 per hour
tutoring. Last week Ajay worked 2 more hours tutoring than hours washing cars and
earned a total of $60. Write a system of equations that could be used to determine
the number of hours Ajay worked washing cars last week and the number of hours he
worked tutoring last week. Define the variables that you use to write the system.
Let
Let
System of Fiquations
Using equation, the number of hours Ajay spent washing car and tutoring are 2 and 4 hours respectively.
How to represent system of equation?Ajay is working two summer jobs working $8 per hour washing cars and $11 per hour tutoring.
Last week Ajay worked 2 more hours tutoring than hours washing cars and earned a total of $60.
The system of equation that could be used to determine the number of hours Ajay worked washing cars last week and the number of hours he worked tutoring last week can be calculated as follows:
let
x = number of hours washing cars
y = number of hours tutoring
Therefore,
y = 2 + x
Hence,
8(x) + 11(2 + x) = 60
8x + 22 + 11x = 60
19x = 60 - 22
19x = 38
x = 38 / 19
x = 2
Therefore,
y = 2 + 2
y = 4
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Answer:
variables :
Let = w = The number of hours washing car.
let = t = The number of hours tutoring.
system of equations:
8w + 11t = 60
t = w + 2
Step-by-step explanation:
Give a real-life representation of loudness and sound using exponential function.
Using an exponential function, the sound intensity of a noise that is 130 dB is of I = 10 watts/m².
Sound levelThe sound level, in dB, of a sound of intensity given by I is given according to the following equation:
[tex]B = 10\log{\left(\frac{I}{I_0}\right)}[/tex]
In which [tex]I_0[/tex] is the smallest sound heard by the human ear, which is of [tex]I_0 = 10^{-12}[/tex] watts/meter.
Hence, for a sound of 130 db, the intensity I is found as follows:
[tex]130 = 10\log{\left(\frac{I}{10^{-12}}\right)}[/tex]
Isolating the logarithm, the equation is:
[tex]\log{\left(\frac{I}{10^{-12}}\right)} = 13[/tex]
The power of 10 and the logarithm are inverse functions, hence the power of 10 is applied to both sides of the equation to isolate the intensity creating the exponential function given as follows:
[tex]10^{\log{\left(\frac{I}{10^{-12}}\right)}} = 10^{13}[/tex]
[tex]\frac{l}{10^{-12}} = 10^{13}[/tex]
[tex]l = 10^{-12} \times 10^{13}[/tex]
Multiplying two terms with the same base and different exponents, we keep the base and add the exponents, hence the intensity is given as follows:
I = 10 watts/m².
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irections: Find the missing endpa
D. R(-9, 4) and S(2, -1); Find T.
The coordinates of T are (13, -6) which s is the midpoint of rt r(-9,4) and s(2,-1).
What is Midpoint?A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.
Let two points A (x₁, y₁) and B (x₂, y₂), the midpoint between A and B is given by,
M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
Assuming that S is the midpoint of the line segment RT, where point R's coordinates are (-9, 4) and S's coordinates are (2, -1).
We have to determine the coordinates of point T.
The midpoint is the average of both endpoints. i.e., (x₁, y₁) and (x₂, y₂).
In this case, the midpoint is given by M = S(2, -1).
Let R(x₁, y₁) = R(-9, 4) and we will determine T(x₂, y₂).
2 = (-9 + x₂)/2
-9 + x₂ = 4
x₂ = 13
-1 = (4 + y₂)/2
4 + y₂ = -2
y₂ = -6
Therefore, the coordinates of T are (13, -6).
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The question seems to be incomplete the correct question would be
Find the missing endpoint if s is the midpoint of rt r(-9,4) and s(2,-1) ; find T
Algebra Question, please provide a step-by-step explanation.
Answer:
4 seconds
Step-by-step explanation:
First I substitute the Y with 0 and then I move the 16x^2 to the left side of the equation and then I divide both sides with 16 leaving me with x^2 then I get the square root of both sides and then I evaluate it and then I got the answer x = 4
Answer:
4 seconds
Step-by-step explanation:
We have a quadtratic equation, that is, we have a function to the highest degree of x^2.
When solving this, we can either solve using the quadratic equation, or by solving for X which would be the easiest and quickest way to do it.
256 -16x^2=0
-16x^2=-256
x^2=16 (divide both sides by -16)
[tex]\sqrt{x} =\sqrt{16}[/tex]
Which leaves x=4 as your answer.
To check this, we can simply input 4 back into the equation, and we will find that it does indeed equal 0.
To further visualize this, when we solve the equation for x, we are finding where the x value that intersects the x axis. We are finding where x=0, or when it touches the ground.
Ryan invests $7,000 for 9 months at a simple interest rate of 8.3%. The amount of interest received is found by
I=PRT
Since R=0.083,
I=0.083 x P x T
What are P and T?
P, which is the principal invested is $7,000 whereas the T is 0.75
What is simple interest?
The simple interest on an investment such as that of Ryan, can be determined as the principal multiplied by the simple interest rate and the time whose formula is as given below:
I=PRT
I=simple interest amount in dollars=unknown
P=principal investment=actual amount invested on simple interest basis=$7000
R=annual simple interest rate=8.3%
T=period of investment measured in years=9/12=0.75(9months divided by 12months in a year gives 0.75 years)
I=$7000*0.083*0.75
I=$435.75
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Armand plans to save money every month for the next six months. The function f(x)=2x−1 represents the amount of money, in dollars, Armand will deposit into his savings account at the end of x months since the time he started saving. Which of the following represents the amount of money, in dollars, Armand deposits into his savings account at the end of 3 months since the time he started saving? Select all that apply. Responses f⋅3f times 3 f(3)f of 3 3f(x)3 f x 23−12 cubed minus 1 3(2x−1)3 times open paren 2 to the x th power minus 1 close paren
AAnswer:
Step-by-step explanation:
Write the following expression using the fewest possible terms.
(−2x − 13) + (19 + 5x)
3x + (−6)
7x + (−6)
7x + 32
3x + 6
There is nothing more we can do with these binomials, so we break them up and combine like terms.
-2x - 13 + 19 + 5x
5x - 2x + 19 - 13
3x + 19 - 13
3x + 6
Answer:
[tex]\boxed{\sf 3x+6}[/tex]
Step-by-step explanation:
[tex]\sf \left(-2x-13\right)+\left(19+5x\right)[/tex]
Simplify:-
[tex]\sf -2x-13+19+5x[/tex]
Combine like terms/Add numbers:-
[tex]\sf -2x+5x-13+19[/tex]
[tex]\sf (-2x+5x)=\bf 3x[/tex]
[tex]\sf (-13+19)=\bf 6[/tex]
[tex]\boxed{\sf 3x+6}[/tex]
Therefore, your answer is D. 3x + 6!!
_______________________
Hope this helps!
Have a great day!
A projectile is fired vertically upward and can be modeled by the function h(t)=−16t2+900t+175. During what time interval will the projectile be more than 9000 feet above the ground? Round your answer to the nearest hundredth.
Calculating a projectile's vertical upward firing is possible using the function h(t)=-16t²+900t+175. 12.65<t<43.59 will the projectile be above the ground at a height more than 9000 feet.
Given that,
Calculating a projectile's vertical upward firing is possible using the function h(t)=-16t²+900t+175.
We have to find how long will the projectile be above the ground at a height more than 9000 feet.
Answers should be rounded to the closest hundredth.
The function is
h(t)=-16t²+900t+175
-16t²+900t+175>9000
-16t²+900t+175-9000>0
-16t²+900t-8825>0
The simplest method for locating a quadratic equation's roots is the quadratic formula. There are some quadratic equations that are difficult to factor, and in these cases we can quickly discover the roots by using the quadratic formula.
Gives the roots of a quadratic equation ax² + bx + c = 0.
x = [-b ± √(b² - 4ac)]/2a.
Now, We get
t= [-900 ± √((900)² - 4(-16)(-8825))]/2(-16)
t=[-900 ± √(810000-564800)]/-32
t=[-900 ± √(245200)]/-32
t=[-900 ± 495.17]/-32
First,
t=[-900 + 495.17]/-32
t=[-404.83]/-32
t=12.65
Second,
t=[-900 - 495.17]/-32
t=[-1395.17]/-32
t=43.59
Therefore, 12.65<t<43.59 will the projectile be above the ground at a height more than 9000 feet.
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Make g the subjest of a=g+h/2
g = a - [tex]\frac{h}{2}[/tex]
2. A car is going 65 miles per hour down the highway.
a. How far does it travel in 1.5 hours?
b. How long does it take the car to travel 130 miles?
c. Mai wrote the equation y = 65x, with a representing
the time traveled, in hours, and y representing the
distance traveled, in miles. Explain why Mai's equation
matches the story.
C
t
a
m
e
th
d
d
a. A car travels 97.5 miles in 1.5 hours.
b. A car takes 2 hours to travel 130 miles.
c. Mai's equation matches the story because it is algebraic form of the formula of speed.
In this question, we have been given a car is going 65 miles per hour down the highway.
Part a.
A car is going 65 miles per hour.
This means, in 1 hour car traveled 65 miles.
Let car travels 'm' miles in 1.5 hours.
So, m = 1.5 × 65
m = 97.5 miles
Thus, a car travels 97.5 miles in 1.5 hours
Part b.
Suppose that it will take t hours to travel 130 miles.
We have been given 1 hour = 65 miles
So, we get an equation,
t = 130 / 65
t = 2 hours
This means, a car takes 2 hours to travel 130 miles.
Part c.
Mai wrote the equation y = 65x, with x representing the time traveled, in hours, and y representing the distance traveled, in miles.
We know that the formula of speed.
speed = distance / time
⇒ distance = speed × time
here, speed = 65 miles per hour
⇒ distance = 65 × time
Assuming distance = y and time = x
y = 65x
This means, Mai's equation matches the story.
Therefore, a. A car travels 97.5 miles in 1.5 hours.
b. A car takes 2 hours to travel 130 miles.
c. Mai's equation matches the story because it is algebraic form of the formula of speed.
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Ashley babysits for 6 hours for $73.50 on Friday and for 3 hours for $36.75 on Sunday. What constant of proportionality relates the number of hours and total pay?
Group of answer choices
$13.50
$12.25
$11.75
$14.25
Answer:
12.25
Step-by-step explanation:
Sonia takes a 4/5-mile walk every day. What part of her walk has she completed once she has walked 3/5 mile?
3/4mile part of her walk completed by Sonia once she has walked 3/5 mile of 4/5 mile distance.
As given in the question,
Sonia takes a walk everyday which is equal to
= 4/5 mile
Moreover, she has completed a part of her daily targeted distance = 3/5 mile
We need to find, what part of the total distance which Sonia covers daily, has she covered just now by covering 3/5 mile of distance.
Part of the total distance which Sonia covers daily, from the distance she has covered just now by covering 3/5 mile of distance
= (Distance covered by Sonia)/ (Total distance covered by Sonia)
= (3/5) / (4/5)
= (3/5) × (5/4)
= 3/4 mile
Therefore,, 3/4mile part of her walk completed by Sonia once she has walked 3/5 mile of 4/5 mile distance.
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plss someone help me asap!!
By analyzing the geometric system, the measure of the angle RSP is equal to 49°.
What are the variables behind the angles of the system of triangles and one of the internal angles
In this problem we find a geometric system formed by two triangles, in which the line segment QR is parallel to the line segment PS. Then, we can obtain the following system of linear equations:
Intern alternate angles between parallel line segments
m ∠ QRP = m ∠ RPS
5 · y + 14 = 8 · y - 13
27 = 3 · y
y = 9
Internal angles of a triangles
m ∠ RPS + m ∠ PRS + m ∠ RSP = 180°
(8 · y - 13) + 3 · x + (2 · x + 1) = 180
8 · y + 5 · x - 12 = 180
8 · y = 180 + 12 - 5 · x
5 · x = 192 - 8 · y
x = (192 - 8 · y) / 5
x = (192 - 8 · 9) / 5
x = (192 - 72) / 5
x = 120 / 5
x = 24
Finally, the measure of the angle RSP is:
m ∠ RSP = 2 · x + 1
m ∠ RSP = 2 · 24 + 1
m ∠ RSP = 49
The measure of the angle RSP is equal to 49°.
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over the set of integers factor the expression 4x^3 - x^2+16x-4 completely
The factorized expression of the equation of the function given as lf(x) = 4x³ - x² + 16x - 4 is f(x) = (x² + 4)(4x - 1)
How to determine the factor of the expression?The equation of the function is given as
f(x) = 4x³ - x² + 16x - 4
Factor out x from the equation of the function
So, we have
f(x) = 4x³ - x² + 16x - 4
Group the terms in 2's
f(x) = (4x³ - x²) + (16x - 4)
Factorize the expression in the bracket
So, we have
f(x) = x²(4x - 1) + 4(4x - 1)
Factor out 4x - 1
So, we have
f(x) = (x² + 4)(4x - 1)
Hence, the factorized expression is f(x) = (x² + 4)(4x - 1)
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Factorise 12x raise to power of 2 and y raise to power of 2 +11xy-5
According to the solving the factorized value of the given equation is:
(4x-5). (3x+1).
What is factorization?Writing a number or any mathematical object as the sum of several factors—typically smaller or simpler objects that use the same known as factorization or factoring. For instance, 3 5 factors the polynomial x2 - 4 as well as the integer 15.
Why do we factor?Factoring is a crucial procedure that aids in our understanding of our equations. We factorize our polynomials to create a simpler form, and when we factorize equations, we obtain a wealth of important information.
According the given data:Detailed explanation:
12x² - 11x-5
12x²+4x-15x-5
4x(3x+1) - 5(3x+1)
(4x-5). (3x+1)
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(p+2) is a factor of (3p^3-4p^2-13p+14)
Answer:
true
Step-by-step explanation:
3p^3-4p^2-13p+14 = (p-1)(3p-7)(p+2)
How do yu solve this problem right here 25m^2 - 17= -1
Answer:
The answer will be 4/5
Step-by-step explanation:
25m^2-17=-1
25m^2=-1+71
√25m^2=√16
5m=4
m=4/5
The division law of exponents says that if b is a non zero number and n and m are any numbers then bm/bn = bm-n true or false?
it is True that the division law of exponents says that if b is a non zero number and n and m are any numbers in the exponents of b then b^m/b^n = b^(m-n)
What is division law of exponents?This is the law that governs numbers that are have exponents or power.
According to the question b is the number while m and n represents the value of the exponents or the numbers for which number b is raised to their power say: b^m and b^n
The division law of exponents holds as:
= b^m ÷ b^n
= b ^ ( m - n )
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in the given picture, the measure of x is __°
*no multiple choice*
Answer:
x = 52°
Step-by-step explanation:
Exterior Angle Theorem
The interior angles of a triangle sum to 180°. Angles on a straight line sum to 180°. Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
⇒ x + 90° = 142°
⇒ x + 90° - 90° = 142° - 90°
⇒ x = 52°
Let us assume that,
→ x + y + 90° = 180°
Now the required value of y is,
→ y + 142° = 180°
→ y = 180° - 142°
→ [ y = 38° ]
Then the value of x will be,
→ x + 38° + 90° = 180°
→ x = 180° - 128°
→ [ x = 52° ]
Hence, the value of x is 52°.
Rory has a handful of Skittles. He has 5 red, 8 yellow, 6 purple, 4 green, and 11 orange.
What is the ratio of red and orange to the other Skittles?
The most appropriate choice for ratio will be given by-
Ratio of red and orange to the other Skittles = 8 : 9
What is ratio?
Ratio determines how many times one number is bigger than the other number, provided both the numbers has the same unit.
The first part of the ratio is called antecedent and the second part of the ratio is called consequent
Here,
Number of red Skittles Rory has = 5
Number of yellow Skittles Rory has = 8
Number of purple Skittles Rory has = 6
Number of green Skittles Rory has = 4
Number of orange Skittles Rory has = 11
Total number of red and orange skittles = 5 + 11
= 16
Total number of other skittles = 8 + 6 + 4
= 18
Ratio of red and orange to the other Skittles = 16 : 18
= 8 : 9
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Yessenia works at The Buckle. She earns $350 per week plus 3% commission on her sales. If Yessenia sells $8,500 worth of clothing this week,
what would her hourly rate be if she worked 40 hours?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
The total amount earned in a week including the commission is $605 working for 40 hours.
The hourly rate is $15.125.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
The amount earned in a week = $350
Amount earned in commission = 3% of $8,500
= 3% of 8500
= 3/100 x 8500
= 3 x 85
= $255
The number of hours worked = 40 hours.
The hourly rate for the week:
= (350 + 255) / 40
= 605 / 40
= $15.125
Thus,
The hourly rate is $15.125.
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11.04 = 1/2 (a + 0) 1.5
Answer: the value of a = 14.72 and if you evaluate it.
Have a good day
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Please use a picture to show where they are plotted if you can.
The slope of the line in the given diagram = rise/run = 1/2.
How to Determine the Rise and Run of a Line to Determine its Slope?The slope of a line is determined as the ratio of the rise of the line to the run of the line.
The rise of a line = change in y
The run of a line = change in x.
The red line in the image attached below shows the rise of the line which is, 1 units.
The blue line represents the run, which is, 2 units.
The slope of the line = 1 units/2 units = 1/2.
Therefore, we can state that the slope of the line = 1/2.
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Solve for x 6 + 2x = 2(x - 3)
Answer:
No solution
Step-by-step explanation:
6 + 2x = 2(x - 3)
6 + 2x = 2x-6
No solution
Which statement is true
A)Only graph A is a function
B)Only graph B is a function
C)Both graphs are functions
D)Neither graph is function
Answer:wish i could help
Step-by-step explanation:......
PLEASE HELP!! PICTURE INCLUDED!!
Please explain how to find angle R!!
Answer:
∠ R = 75°
Step-by-step explanation:
you are correct with answers to a, b, c
d
the sum of the 3 angles in Δ QRS = 180° , that is
∠ Q +∠ R + ∠ S = 180° , so
55° + ∠ R + 50° = 180°
∠ R + 105° = 180° ( subtract 105° from both sides )
∠ R = 75°
23. graph 6x=-90
pls anwser need to turn in asap
Answer:
Step-by-step explanation:
Step: 1
-Graph the 6x: It will start at (0,0) and will have a rise of 6 and a run of 1
Step: 2
-Graph the 90: From what I understand it should be a horizontal line with its point on 90y
Sorry if this doesn't help very late where I am.
Line g passes through points (2, 3) and (5, 2). Line h is perpendicular to line g. What is the slope of line h?
The slope of the line h is 3
Let m1 be the slope of line g and m2 be the slope of line h.
Line g passes through points (2, 3) and (5, 2).
Using the formula of slope,
m1 = (2 - 3)/(5 - 2)
m1 = -1 / 3
Line h is perpendicular to line g.
We know that the product of slopes of the perpendicular lines is -1.
m1 * m2 = -1
(-1/3) * m2 = -1
m2 = 3
Therefore, the slope of the line h is 3
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