The number of miles to drive for 30 gallons is 960 miles
How to determine the function value?From the question, the function definition is given as
d(g) = 32g
Where g represents the number of gallons and d represents the distance
The function value to calculate is given as
d(30)
This means that we calculate the number of miles to drive for 30 gallons
So, we have
d(30) = 32(30)
This gives
d(30) = 32 x 30
Evaluate the product
d(30) = 960
Hence, the function value is d(30) = 960
Read more about functions at
https://brainly.com/question/28532394
#SPJ1
If ax-3=bx+5 then the solution for x in terms of a and b is
In this equation the solution for x in terms of a and b is 8.
What is equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
Sol- As per the question given that- ax-3= bx+5------(equation 1)
Let ax=3-----(equation 2)
And bx =5------(equation 3)
On adding equation(1)and (2) we get
(ax)+(bx)= 3+5
(ax)+(bx)=8
x(a+b)+y(a+b)=8
(x+y)+(a+b)=8
1×(a+b)=8
Thus
a+b=8
To know more about equation click -
https://brainly.com/question/2972832
#SPJ13
Chad doesnt have any money, but he owes his sister $15, owes his brother $9 and owes his friend $24. What integer could be used to represent the amount of money chad has?
Answer:
- 48.00
Step-by-step explanation:
Add all the debt up.
Answer: -48
Step-by-Step Explanation:
Money that Chad owes his Sister = $15
Money that Chad owes his Brother = $9
Money that Chad owes his Friend = $24
Total Money he owes = 15 + 9 + 24 = $48
Hence, Total Money he has = -48 (since he doesn't have any money)
I have a graph with the question. If the parent function is y= 2 to the power of x plus 2, which is the function of the graph
The parent function of the graph is
[tex]y=2^x[/tex]The function of the grapg will be
[tex]y=2^{x\text{ + a}}\text{ + b}[/tex]at x equals infinity y equals 1
Therefore
[tex]\begin{gathered} \text{x =}\infty\text{ then y = 1} \\ \text{this implies} \\ b\text{ = 1} \end{gathered}[/tex]Therefore the function will now be
[tex]y=2^{x\text{ + a}}\text{ + 1}[/tex]from the graph
x = 2 when y = 2
Therefore,
[tex]\begin{gathered} 2=2^{2\text{ + a}}\text{ + 1} \\ 2-1=2^{2\text{ + a}} \\ 1=2^{2\text{ + a}} \\ \text{recall 1 = 2}^0 \\ 2^0=2^{2\text{ + a}} \\ 2\text{ + a = 0} \\ a\text{ = - 2} \end{gathered}[/tex]Therefore, the function is
[tex]y=2^{x\text{ - 2}}\text{ + 1}[/tex]I need help with this math question all parts please
we have the function
[tex]P(t)=\frac{60(1+0.4t)}{0.01t+3}[/tex]Part A
For t=0
substitute
[tex]\begin{gathered} P(t)=\frac{60(1+0.4(0))}{0.01(0)+3} \\ \\ P(t)=\frac{60(1)}{3} \\ \\ P(t)=20 \end{gathered}[/tex]The initial population was 20 insectsPart B
For t=5 years -------> Convert to months
t=60 months
substitute
[tex]\begin{gathered} P(t)=\frac{60(1+0.4(60))}{0.01(60)+3} \\ \\ P(t)=\frac{60(1+24)}{0.6+3} \\ \\ P(t)=\frac{1500}{3.6} \\ \\ P(t)=416.67 \end{gathered}[/tex]The answer is 417 insectsPart C
Determine horizontal asymptote
[tex]\begin{gathered} P(t)=\frac{60\left(1+0.4t\right)}{0.01t+3} \\ \\ rewrite \\ P(t)=\frac{60+24t}{0.01t+3} \end{gathered}[/tex]The horizontal asymptote is given by the ratio of
[tex]\frac{24}{0.01}=2,400[/tex]P(t)=2,400 ---------> horizontal asymptote
that means
as the value of time t increases ------> the value of the population tends to 2,400 insects
the population cannot be greater than 2400 insects
The range for the function P(t) is the interval [20, 2400)
All real numbers greater than or equal to 20 insects and less than 2400 insects
Part D
Using a graphing tool
find the volume of the rectangular prism. need an integer or decimal.
We will have the following:
[tex]V=(\frac{9ft\ast9ft}{2})(12ft)\Rightarrow V=486ft^3[/tex]So, the volume is 486 ft^3.
What is the image point of (-7,3) after the transformation rx-axis o R180º?
In a composite transformation as given you make first the transformation in the right and then the transformation in the left.
For the given point: (-7, 3)
1. Rotation 180°
[tex]\begin{gathered} P(x,y)\rightarrow P^{\prime}(-x,-y) \\ \\ P(-7,3)\rightarrow P^{\prime}(7,-3) \end{gathered}[/tex]2. Reflection over x-axis:
[tex]\begin{gathered} P^{\prime}(x,y)\rightarrow P^{\prime}^{\prime}(x,-y) \\ \\ P^{\prime}(7,-3)\rightarrow P^{\doubleprime}(7,3) \end{gathered}[/tex]Then, the image of given point after the composite transformation is (7,3)Write an exponential expression equivalent to 8^3 that has a base of 2.
The exponential expression equivalent to 8^3 that has a base of 2 is 2^9.
What is exponential expression?
Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied.
Applying the laws of indices,
The expression 8^3 can be written as,
8 x 8 x 8 = (2^3) x (2^3) x (2^3)
= 2^(3+3+3) ...{If a^m x a^n then a^(m+n) }
8 x 8 x 8 = 2^9
Therefore, the exponential expression equivalent to 8^3 that has a base of 2 is 2^9.
To know more about the exponential expressions, click on the link
https://brainly.com/question/28200743
#SPJ13
Solve the inequality and graph the solution on the line provided.
3x+17_< 41
What is the slope of the line x=4?
O A. 0
O B. Undefined
O C. 4
• D.1
Answer:
B. Undefined
Step-by-step explanation:
x = 4 is a vertical line, and vertical lines are Undefined because they go straight up.
vAt her Fourth of July party, Sally serves her famous grilled chicken. Her secret is to use 6 fluid ounces of lemon-garlic marinade for every pound of chicken. Sally plans to grill 4 pounds of chicken. How many cups of marinade should she use
In linear equation, 3 number of cups will be needed to marinade 4 pounds of chicken for grill.
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.Here we have the data from the question:-
Marcy will use 6 fluid ounces of lemon-garlic marinade for every pound of chicken.
Marcy plans to grill 4 pounds of chicken.
So total marinade required will be:-
Total marinade =6x4=24 ounces
Now we know that the conversion:-
1 fluid Ounce = 0.125 Cup
24 fluid ounce =0.125 Cup
Hence 3 number of cups will be needed to marinade 4 pounds of chicken for grill.
Learn more about linear equation
brainly.com/question/11897796
#SPJ10
Each person gets 3 scoops of ice cream. Is this relationship between the number of people and the number of scoops proportional?
Yes, the number of scoops proportional.
Define Proportional
A linear relationship between two amounts or variables is indicated by proportionality. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.
Hence, It is proportional. This is because as the number of people increases, the number of scoops also increase.
To read more about the Proportional.
https://brainly.com/question/19994681
#SPJ13
What is the value of logx?y3lodwhen given the following:Zlog(x) = 3log(y)=2log(z)= -1
Given the question
[tex]\log (\frac{x^2y^3}{z})[/tex]To resolve this, we can follow the steps below
Step1: Apply the logarithm rule
[tex]\log (\frac{x^2y^3}{z})=\log x^2+\log y^3-\log z[/tex]This will give=>
[tex]\log x^2+\log y^3-\log z=2\log x+3\log y-\log z[/tex]Since we have been given that
[tex]\begin{gathered} \log x=3 \\ \log y=2 \\ \log z=-1 \end{gathered}[/tex]Step2: Substitute the given values into the equation
[tex]2\log x+3\log y-\log z=2(3)+3(2)-(-1)[/tex]=>
[tex]6+6+1=13[/tex]Answer = 13
The larger of two numbers is five times the difference of the small number and one. If sum of the two numbers is 50 what are the two numbers?
Answer:
Step-by-step explanation:
40.833 recurring and 9.166 recurring
or 40 5/6 and 9 1/6
Call the small number 's'
Call the big number 'b'
The word problem says:
B+S=50 and also that 5(S-1)=B which multiplied out is 5S-5=B
So, 5S-5=B=50-S
Therefore 6S=55 and the rest history!
Answer:
Step-by-step explanation:
HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP
Find the area of 2x-9 + x+5
Answer: 3x-4
Step-by-step explanation: First Simplify, add the numbers 2x-9+x+5=2x-4+x Then combine like terms, 2x-4+x= 3x-4
Find the midpoint of the segment below and enter its coordinates as anordered pair. If necessary, express coordinates as fractions, using the slashmark (/) for the fraction bar.
Each midpoint's coordinate is given by the mean of the respective coordinates of the two endpoints of the segment. Then, if we say M is the midpoint of that segment, we have:
Mx = (-4 + 4)/2 = 0/2 = 0
My = [6 + (-2)]/2 = (6 - 2)/2 = 4/2 = 2
Therefore, writing those coordinates as an ordered pair, we have:
M = (0, 2)
Solve using substitution.
X = 7
-2x 9y = 13
(__ , __)?
Submit
Answer:
(7,-3)
Step-by-step explanation:
x = 7
-2x - 9y = 13
* Substituition is the easieat way to solve such a function.
- Firstly, put "7" instead of "x" in the equation.
- multiply "7" by "-2"
- Solve for "y"
* -2x-9y = 13
* -2×7-9y = 13
* -14-9y = 13
* -9y = 27
* -9y/-9 = 27/-9
* y = -3
# Since x = 7, the output/"y" will be -3
(7,-3)
this is a little hard for me help me out please
The simplified form of the expression as a fraction is -43/390.
Solving expressions and simplifying fractionsFractions are expression written as a ratio of two integers. For instance, a/b are known as fractions.
Given the expression below:
[2-|-2/3-2(-1/5)|]÷(-13)
In order to solve the expression, we will use the PEMDAS rule to have:
[2-|-2/3-2(-1/5)|]÷(-13)
[2-|-2/3+1/10)|]÷(-13)
Find the LCM
[2-|-20+3/30|]÷(-13)
[2-|-17/30|]÷(-13)
[2-(17/30)]÷(-13)
[60-17/30]÷(-13)
43/30÷(-13)
Change the division sign to multiplication
43/30÷(-13)
43/30 * -1/13
-43/390
This gives the simplified form of the expression.
Learn more on simplifying expressions here: https://brainly.com/question/28036586
#SPJ1
a potter forms a piece of clay into a right circular cylinder. as she rolls it, the height of the cylinder increases and the radius decreases. assume that no clay is lost in the process. suppose the height of the cylinder is increasing by centimeters per second. what is the rate at which the radius is changing when the radius is centimeters and the height is centimeters?
The radius of the cylinder is decreasing at the rate of 0.22 cm per second.
One of the most important and fundamental curvilinear of a geometric shapes, a right circular cylinder has historically been a three-dimensional solid.
It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.The radius of the cylinder is the length of the line joining the circumference and the center of the circle.The derivative of the logarithm, dx /dt, is also the growth rate. The fractional change, must be used to represent a minor change in the logarithm. if the variable grows at the constant fixed rate g.Volume of a right circular cylinder = π r² h
Now we differentiate w.r.t to get :
[tex]\frac{dV}{dT} =2 \pi r h\frac{dr}{dt} + \pi r^2\frac{dh}{dt}[/tex]
Taking the values we get :
[tex]-34.3 = 154 \frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt} = -0.22[/tex]
Hence the radius is decreasing at the rate of -0.22 cm per second.
To learn more about cylinder visit:
https://brainly.com/question/16134180
#SPJ4
PLEASE ANSWER QUICK IT IS THE LAST PROBLEM ON HERE AND IT IS DUE TODAY!!!
Answer should be inequality!
Ray had scores of 75, 82, 94, and 77 on his first four algebra tests. What must he score on the next test to have an average of at least 85?
Please show work as well if possible.
Answer:
x ≥ 97
Step-by-step explanation:
Average = Sum of values divided by the amount of numbers in a data set
Data Set: {75, 82, 94, 77, ?}
75 + 82 + 94 + 77 + ? = ? ÷ 5 = 85
85 x 5 = 425
75 + 82 + 94 + 77 + ? = 425 ÷ 5 = 85
75 + 82 + 94 + 77 = 328
425 - 328 = 97
Ray must score greater than or equal to 97, or x ≥ 97 in order to have an average of at least 85.
Choose a relationship model that will reach $0 in the same number of days as this scenario: mika has $12 and spends $2 each day. y = â€""2x â€"" 12 y = â€""3x 18 y = â€""4x 12 y = â€""12x 2
The equation that represent the relationship model that will reach $0 in the same number of days as the scenario gave is: y = -2x + 12
To solve this problem, we have to state the equation using the information of the problem.
Information about the problem:
Mika has = $12Mika spend = $2 per dayDay = xy = $0Writing the equation according to the information gave, we have:
y = -2x + 12
Where:
y = 0$x = daysSo that (y) equals zero, the number of days (x) should be = 6
y = -2x + 12
0 = -2*6 + 12
0 = -12 + 12
0 = 0
The "y" variable is the dependent variable, because it will change according to the number of days passed (x).
The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of days passed.
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Learn more about equation at: brainly.com/question/2972832 and brainly.com/question/27815607
#SPJ4
Sandra purchased $1,200 worth of electronic equipment on her new credit card, with an annual interest rate of 14.99%. If she has no other charges on the card and does not pay off the balance at the end of the month, how much money will she owe the credit card company after 1 month? Estimate the interest using the monthly periodic rate.
Given data:
The given amount of equipment purchased by the Sandra is A=$1,200.
The equation for line s can be written as x - y = -2. Line t is perpendicular to lines and passes through (-4, 1). What is the equation of line t?
=========================================================
Explanation:
Anything perpendicular to Ax+By = C is of the form Bx-Ay = D
The given equation is x-y = -2 showing that A = 1, B = -1 and C = -2.
So Bx-Ay = D will update to -x-y = D
Plug in the coordinates of (-4,1) to find D.
-x-y = D
D = -x-y
D = -(-4)-1
D = 4-1
D = 3
We go from -x-y = D to -x - y = 3
Then multiply both sides by -1 to end up with x + y = -3
Find the value of x.
(8x - 11)
5x°
(2x+6)°
Answer: x=37/3
Step-by-step explanation:
8x-11+5x+2x+6=180 ==> three angles of a triangle add up to 180 degrees
8x+5x+2x-11+6=180
13x+2x-5=180
15x-5=180
15x=185
x=185/15
x=37/3
Please assist Math with 50 points!
Answer:
A. (1/2) bucket
Step-by-step explanation:
6 11
4 ------ - 3 ------- = ?
14 12
14 × 4 = 56
56 + 6 = 62
12 × -3 = -36
-36 - 11 = -47
62 47
------- - -------
14 12
62(12) 47(14)
------- - -------
14(12) 12(14)
744 658 86
------- - ------- = --------
168 168 168
86 ÷ 2
-------
168 ÷ 2
43
----- = 0.511
84
0.511 ≈ (1/2)
I hope this helps!
Answer:
1/2 bucket
Step-by-step explanation:
Please helppp as fast as possible 20 points ***
FIND THE DOMAIN & RANGE OF THE FUNCTION
g(x)=|x + 4|
Please helppp as fast as possible
Answer:
Domain: (−∞,∞),{x | x ∈ R}
Range: [0,∞),{y|y≥0}
Step-by-step explanation:
Given g(x)=−23(x−4)2+3, g ( x ) = − 2 3 ( x − 4 ) 2 + 3 , what is the value of g(–5)? *Type in your answer. g(–5) =
The output value of g( -5 ) in the function g( x ) = −23( x - 4 )2 + 3 is 417.
What is the output value of g(-5) in the given function?A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.
Given the data in the question;
g( x ) = −23( x - 4 )2 + 3g( -5 ) = ?To find the g( - 5 ), replace all the occurrence of x with -5 in the function and simplify.
g( x ) = −23( x - 4 )2 + 3
g( -5 ) = −23( -5 - 4 )2 + 3
g( -5 ) = −23( -9 )2 + 3
g( -5 ) = −23( -9 × 2) + 3
g( -5 ) = −23( -18) + 3
g( -5 ) = ( -23 × -18) + 3
g( -5 ) = ( 414 ) + 3
g( -5 ) = 414 + 3
g( -5 ) = 417
Therefore, the output value of g( -5 ) is 417.
Learn more about functions here: brainly.com/question/2541698
#SPJ1
can you explain each step please for i can write it on a paper along with you
The two groups are given one is those who are studied and other is those who are not studied.
Studied - 88,100,94,79,92,100,95,83,89,99,100,91,89,95,100,93,96,84.
Arrange in order.
79, 83, 84, 88, 89, 89, 91, 92, 93, 94, 95, 95, 96, 99, 100, 100, 100, 100
The mean of this group is
[tex]\frac{88+100+94+79+92+100+95+83+89+99+100+91+89+95+100+93+96+84}{18}[/tex][tex]\frac{1667}{18}=92.6[/tex]The mean is 92.6.
The median of this group is
Use the median formula for even
[tex]m=\frac{(\frac{n}{2})^{th}+(\frac{n}{2}+1)^{th}^{}}{2}[/tex]Substitute the value of n =18
[tex]m=\frac{(\frac{18}{2})^{th}+(\frac{18}{2}+1)^{th}^{}}{2}=\frac{9^{th}+10^{th}^{}}{2}[/tex][tex]m=\frac{93+94}{2}=93.5[/tex]The median is 93.5.
The mode of this group is 100 as it is appears 3 times .
The another group is not studied group.
Not studied - 82,72,45,91,58,83,65,87,90,77,73,89.
Arrange in order-
45, 58, 65, 72, 73, 77, 82, 83, 87, 89, 90, 91
The mean is determined as
[tex]\frac{82+72+45+91+58+83+65+87+90+77+73+89}{12}=\frac{912}{12}=76[/tex]The median is determined as
[tex]m=\frac{(\frac{n}{2})^{th}+(\frac{n}{2}+1)^{th}}{2}[/tex]Substitute n=12.
[tex]m=\frac{(\frac{12}{2})^{th}+(\frac{12}{2}+1)^{th}^{}}{2}=\frac{6^{th}+7^{th}}{2}=\frac{77+82}{2}=79.5[/tex]There is no mode.
So, from the all the data given.
The mean of the group that studied is over 15 percent points higher than the mean of the group that did not studied.
[tex]92.61-76=16.61[/tex]The median of the group that did not studied is less than 80.
In general , those students that studied scored much higher than those students that did not study.
The correct options are a , c and e.
si cada 8.33 minutos me dan 10 dolares cuantos dolares tendria en 6 horas ademas cuantos dolares ganaria cada 30 minutos
The payment for each 6 h is equal to $ 432.2 while the payment for each 30 min would be $ 36.01.
Rule of ThreeIt's a math tool for solving problems about proportion. You can relate more than 2 variables and from the proportion, it's possible to find an unknown number.
Conversion Unit TimeIn the International System Units (SI), the standard unit for time is the second (s). For solving any exercise, you need to know the relation between the units of the time. See below:
1h=60 min = 3600s
1 min = 60 s
Now you can solve the question from the rule of three for finding the payment in dollars.
The question gives: an each 8.33 min, the payment is 10 dollars. Thus, from this relation you can write:
For 6 hFirst, you should convert 6h to minutes, then,
1 h ----- 60 min
6h ----- x
x=60*6=360 min
After that, you should apply the rule of three for finding the payment in dollars.
8.33 min ----- 10 dollars.
360 min ------- x
8.33x=360*10
8.33x=3600
x= $ 432.2
For 30minYou should apply the rule of three for finding the payment in dollars.
8.33 min ----- 10 dollars.
30 min ------- x
8.33x=30*10
8.33x=300
x= $ 36.01
Read more about the rule of three here:
brainly.com/question/24514897
#SPJ1
what is the missing measurement (w) for the poster of spongebob.
To make a poster you have to keep the ratio between lenght and height (otherwise it will look weird)
This is:
[tex]\frac{12\operatorname{cm}}{20\operatorname{cm}}=\frac{w}{36\operatorname{cm}}[/tex]