Answer:
see explanation
Step-by-step explanation:
this can be expressed in ratio form and fractional form , that is
45 : 30 ( divide each part by 15 )
= 3 : 2 ← in simplest form
= [tex]\frac{3}{2}[/tex]
Question 7
Let f (x) = -2x³ + ax² +2. You are told that f (2) = 14, what is the value of a ?
a=9
a=8
a=7
a=6
Answer:
a = 7
Step-by-step explanation:
Substitute x for 2 and f(x) for 14
14 = -2(2³) + a(2²) + 2
14 = -16 + 4a + 2
14 = -14 + 4a
14 + 14 = 4a
28 = 4a
4a = 28
Divide both sides by 4
4a/4 = 28/4
a = 7
Alternative:
Since from the question, you're already told that f(2) = 14, you just have to find the number that can be multiplied by 2 with a resultant of 14; that number is 7. To confirm, substitute a for 7 in the equation.
The resistance of a thermistor, a device used to monitor the temperature inside an engine, changes with temperature. The resistance of the thermistor is given by R(t) = t3 + 5, where R is measured in ohms and t is the temperature in °C. What is the average rate of change of resistance per degree of temperature change between 0°C and 2°C?
A.
4 ohms/°C
B.
8.5 ohms/°C
C.
11 ohms/°C
D.
17 ohms/°C
Answer: In photo below
You're Welcome :)
The average rate of change of the resistance of the thermistor for each degree change in the temperature, when the temperatures changes from 0 °C and 2 °C is A. 4 ohms/°C
What is the average of a set of values?The average is calculated by adding the values in the dataset then dividing the result by the count of the numbers or values in the set. The average is also known as the arithmetic mean.
The function for finding the resistance of the thermistor is; R(t) = t³ + 5
The unit of the R = Ohms
The unit of t = Degrees Celsius, °C
The resistance of the thermistor when the temperature is t = 0 °C is found as follows;
R(0) = 0³ + 5 = 5
Therefore;
When the temperature is 0 °C the resistance of the thermistor is 5 Ohms
When the temperature is t = 2 °C, we have;
R(2) = 2³ + 5 = 13
The resistance of the thermistor at t = 2 °C is 13 Ohms
The average rate of change of a function, f(x), is found using the formula;
[tex]A(x) = \dfrac{f(x_2) - f(x_1) }{x_2-x_1}[/tex]
The average rate of change of the resistance per degree change in the temperature, between the temperature interval of 0 °C and 2 °C is therefore;
[tex]A(x) = \dfrac{R(2) - R(0)}{2 - 0}[/tex]
Which gives;
[tex]A(t) = \dfrac{13 -5}{2 - 0}= 4[/tex]
The average rate of change of the resistance of the thermistor between the temperatures of t = 0 °C and t = 2 °C is 4 Ohms/°C
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Tritium is a radioactive isotope of hydrogen that decays by about 5% per year. A large bottle of water that contained 856,000 tritium atoms remained undisturbed for 13 years. How much tritium does the bottle contain now?
If necessary, round your answer to the nearest whole number.
tritium atoms
The amount of Tritium that bottle contains now will be 439,421.
What is an exponent?Consider the function:
y = a (1 - r)ˣ
Where x is the number of times this decay occurs, a = initial amount, and r = fraction by which this decay occurs.
Tritium is a radioactive isotope of hydrogen that rots by around 5% each year. An enormous container of water that contained 856,000 tritium iotas stayed undisturbed for a very long time.
Then the amount of Tritium that bottle contains now will be given as,
y = 856,000 (1 - 0.05)¹³
Simplify the equation, then we have
y = 856,000 (1 - 0.05)¹³
y = 856,000 (0.95)¹³
y = 856,000 (0.51334)
y = 439,421
The amount of Tritium that bottle contains now will be 439,421.
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Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the wire they need. Andy needs 24 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?
Step-by-step explanation:
Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the wire they need. Andy needs 24 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?
Looking at your chart:
cost/length in inches
6/100 = $0.06 per inch
8.1/135 = $0.06 per inch
9.6/160 = $0.06 per inch
10.8/180 = $0.06 per inch
So the rate stays at a constant rate of $0.06 per inch.
Andy needs 24 feet or 288 inches at a constant rate of $0.06 per inch.
= 288 * $0.06
= $17.28
________________________________
Emily needs 15 yards or 540 inches at a constant rate of $0.06 per inch.
= 540 * $0.06
= $32.40
The weight, in pounds, of a newborn baby t months after birth can be modeled by the equation W=1.75t+6. What is the slope of the equation and what is its interpretation in the context of the problem?
Answer:
the slope is 1.75
Step-by-step explanation:
Interpretation: The weight of newborn is 6 lb at birth, and every month baby gained 1.75 lb. You replace x with month you want to know the weight. For example you can calculate the weight after 4 month : w= 1.75(4)+6= 13 lb
Created a painting with an area of 48 in.² and a length of 6 inches they create a second painting with an area of 64 in.² it has the same width as the first painting what is the length of the second painting
The length of the second rectangle is 8 in
How to find the length of the second painting?Since we have painting with an area of 48 in.² and a length of 6 inches, since it is a rectangle, its area is A = LW where
L = length of rectangle = 6 in and W = width of rectangleSo, making Wsubject of the formula, we have
W = A/L
Since
A = 48 in² and L = 6 inSubstituting these into the equation, we have
W = A/L
W = 48 in²/6 in
W = 8 in
Now, since the second painting with an area of 64 in.² it has the same width as the first painting, since it is also a rectangle, its area is A = LW where
L = length of rectangle and W = width of rectangleSo, making L subject of the formula, we have
L = A/W
Since
A = 64 in² and W = 8 inSubstituting these into the equation, we have
L = A/W
L = 64 in²/8 in
L = 8 in
So, the length of the second rectangle is 8 in
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The cost to attend a public university in a recent year is $16,241. The circle graph to
the right shows the percentage of that cost for tuition/fees, room, board, and
computer costs. Determine the cost, in dollars, for each category.
The cost of tuition and fees is $.
(Round to the nearest cent as needed.)
The cost of room is $.
(Round to the nearest cent as needed.)
The cost of board is $.
(Round to the nearest cent as needed.)
The computer costs are $
(Round to the nearest cent as needed.)
Cost to Attend a Public University
Tuition/Fees 36.9%
Room 31.5%
Board 24.9%
Computer costs 6.7%
Using the circle graph, the costs to attend the public university are as follows:
cost of tuition and fees = $ 5992.93cost of room = $5115.92cost of board = $ 4044.01computer cost = $1088.15How to find cost using circle graph or pie chart?A circle graph, or a pie chart, is used to visualize information and data.
Therefore, the circle graph is shows the percentage cost for tuition/fees, room, board, and computer costs.
The cost to attend a public university in a recent year is $16,241.
Using the pie chart, let's find the cost of the various fees.
Therefore,
cost of tuition and fees = 36.9% of 16,241
cost of tuition and fees = 36.9 / 100 × 16241
cost of tuition and fees = 599292.9 / 100
Therefore,
cost of tuition and fees = $ 5992.929
cost of room = 31.5% × 16241
cost of room = 31.5 / 100 × 16241
cost of room = $5115.915
Hence,
cost of board = 24.9% of 16241
cost of board = 24.9 / 100 × 16241
cost of board = $ 4044.009
Hence,
computer cost = 6.7% of 16241
computer cost = 6.7 / 100 × 16241
computer cost = $1088.147
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A wasp is 1.39-10 meters long.
A pygmy rabbit is 24-10¹ meters long.
How much langer is the pygmy rabbit than the
wase?
Pygmy rabbit is 22.61-10 meters longer than the wasp.
Given:
A wasp is 1.39-10 meters long.
A pygmy rabbit is 24-10¹ meters long.
Pygmy rabbit longer than the wasp = size of pygmy rabbit - size of wasp.
= (24 - 1.39)-10meters
= 22.61-10 meters.
Therefore pygmy rabbit is 22.61-10 meters longer than the wasp.
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The sum of a number and 4 times the number
Write two equivalent expressions for each statement.
Let the number be n.
Then the expression is:
The sum of a number and 4 times the numbersum = n + 4nsum = 5nAnswer:
4x + x5xStep-by-step explanation:
Forming the expression,
→ 4x + x
Let's solve the expression,
→ 4x + x
→ 5x
Hence, the answer is 5x.
4. Solve the equation m² = 14.
Answer:
m=3.7
Step-by-step explanation:
m²=14
m=√14
m=3.7416573868
m=3.7(2 d.p)
In the middle of a park, there is a fenced off area in the shape of a square with an area of 225 yards. What is the side length of the square? What is the perimeter of the fenced off area?
what is a peremiter
Perimeter meaning: the continuous line forming the boundary of a closed geometric figure.
side length: 15
perimeter: 368
SOMEONE HELP ME.
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. What are the dimensions of this rectangular room in the actual building.
The dimension of the rectangular room in the actual building are 55 feet by 30 feet.
How to find the dimension of the rectangular room in the actual building?Scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building.
The dimensions of this rectangular room in the actual building can be found as follows:
let's find the length of the actual room
1 inches = 10 feet
3 inches = ?
cross multiply
length = 30 ft
Let's find the width of the room
1 inches = 10 feet
5.5 inches = ?
cross multiply
width = 55 ft
Therefore, the width and length of the room are 55 feet and 30 ft respectively.
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Rebecca wants to buy a new phone. She has already saved $110 and received a gift of $50 from her grandmother that she added to her savings. She plans to earn the rest by selling necklaces for $5 each. The phone she wants to purchase costs $485. Write an equation that represents how many necklaces Rebecca will need to sell in order to have enough money to get her phone.
Answer:
5x=325+160
Step-by-step explanation:
this was very easy but i guess with so many words it could confuse people
The equation
Ax+By=−18
A
x
+
B
y
=
−
18
goes through the coordinates (-3, 10) and (6, -2).
By solving a system of equations, we will see that the equation is:
-4*x - 3*y = -18
How to find the equation?We know that the linear equation:
A*x + B*y = -18
We know that this linear equation passes through the points (-3, 10) and (6, -2), then replacing these values in the equation we will get two equations:
A*-3 + B*10 = -18
A*6 + B*-2 = -18
So we have a system of equations:
-3A + 10B = -18
6A - 2B = -18
if we add the two times the first equation and the second one we get:
2*(-3A + 10B) + 6A - 2B = 2*(-18) - 18
18B = -3*18
B = -3
by replacing that value of B in one of the equations we will be able to solve it for A.
6*A - 2*(-3) = -18
6*A + 6 = -18
6*A = -18 - 6 = -24
A = -24/6 = -4
The equation is:
-4*x - 3*y = -18
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Tiffany borrows $8,000 to pay for college. The loan has a 7% interest rate that compounds monthly. She plans to pay off the loan in 15 years. How much will she pay in total?
Tiffany needs to pay $8,084.44 in total.
what is Compound Interest?In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest.
Given:
P= 8000
R= 7%= 0.07
Time= 8 years.
Now, Amount = P[tex](1 + r/n)^{nt[/tex]
Amount = 8000 [tex](1 + 0.07/15)^{12 . 15[/tex]
Amount = 8000 x (1 + 5.8333333333333E-5)
amount = $8,084.44
Hence, Tiffany needs to pay $8,084.44 in total
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which is the correct answer for this ??????
The given system of linear equations has no solution. By solving the equations using substitution method we get (11, 0) where no solution exists.
How many solutions can a system of linear equation can have?
A system of linear equations is usually a set of two linear equations with two variables.
The solution to a system of linear equations is the point at which the lines representing the linear equations intersect.
With linear systems of equations, there are three possible outcomes in terms of number of solutions:
One solutionInfinitely many solutionsNo solutionHow to identify the number of solutions?
Rewrite both equations in slope-intercept form, y = mx + b.
Compare the slopes of the lines, m, and their y-intercepts, b, to determine the number of solutions.
If the two equations have different m-values, then the system has one solution.If the two equations have the same m-value but different b-values, then the system has no solution.If the two equations have both the same m-value and the same b-value, then the system has infinitely many solutions.According to the given question:
Given system of linear equation are: y = -x + 11 and -4x -4y = 44
Rewriting the equations in slope-intercept form
y = -x + 11 ---- 1)-4y = -4x + 44Simplifying further by dividing the equation with -4 on both side
y = x - 11 ------ 2)
Clearly, both the equation have different m-values.
Hence the system of equation have one solution.
Now solving by substitution method
Substituting 2) in 1)
x - 11 = -x + 11 (since y = x -11 from 2))
2x = 22
∴ x = 11
Now substituting x = 11 in equation 2) to get the value of y
y = 11 - 11
∴ y = 0
So, the system of equation has no solution at (11, 0).
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The cost to attend a public university in a recent year is $16,241. The circle graph to
the right shows the percentage of that cost for tuition/fees, room, board, and
computer costs. Determine the cost, in dollars, for each category.
The cost of tuition and fees is $.
(Round to the nearest cent as needed.)
The cost of room is $.
(Round to the nearest cent as needed.)
The cost of board is $.
(Round to the nearest cent as needed.)
The computer costs are $
(Round to the nearest cent as needed.)
Cost to Attend a Public University
Tuition/Fees 36.9%
Room 31.5%
Board 24.9%
Computer costs 6.7%
Answer:
Tuition and Fees = $5,992.93
Room = $5,115.92
Board = $4,044.01
Computer Costs = $1,088.15
WILL GIVE BRAINLIEST !!
What does the slope of a position vs. time graph tell you? What does the slope of a velocity vs. time graph tell you?
Answer:
a) velocity
b) displacement
You rent a bicycle for 20 plus per hour. What is the rate of change
The rate of change for cost is = $2 per hour .
In the question ,
it is given that
the fixed rent for the bicycle is =$20
per hour charge of the bicycle is = $2
let the number of hours we rent a bicycle is = x
and let the total cost for renting the bicycle is = y
So , the equation to represent the cost becomes
y = 20 + 2x
to find the rate of change we differentiate the equation with respect to x .
we get
dy/dx = 2
Therefore , The rate of change is $2 per hour .
The given question is incomplete , the complete question is
You rent a bicycle for $20 plus $2 per hour. What is the rate of change of Cost ?
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Given m || n
find the value of x and y.
(6x+19)° (2y+1)⁰
(3x+8)°
m
n
A value for x is therefore represented by the first number in an ordered pair, and a value for y is represented by the second.The x- and y-coordinates are the names given to these values.
Find the value of x and y ?The Method of Elimination
To ensure that the two equations have the same leading coefficient, multiply each equation by a reasonable number in step one.
Step 2: Reverse the first equation and subtract the second one.
Step 3: Find y using this new equation.
Step 4: Change Equation 1 or Equation 2 above to y = 2 and then solve for x.
multiply the equation y = x - 6 by -6.
You will then get the equation: 6y = -6x + 36
The two equations will be:
6y = -6x + 36
y = 6x - 19
And you can see that if you add them, you will be able to eliminate x. answer is -6.
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Linear regression question 8
Use graph below using all the points on the graph to figure out the line of best fit and the estimate of Carter’s weight 15 weeks into his diet.
The linear regression equation from the given scatter plot is:
y = -1.62x + 215.64.
Using this function, the estimate of his weight 15 weeks into the diet is:
191.34 pounds.
How to obtain the linear regression equation?The linear regression equation is obtained inserting the points of the scatter plot of the situation into a linear regression calculator.
From the given scatter plot, the points are given as follows:
(0,216), (1,214), (2,213), (3,210), (4,210), (5,207), (6,206), (7,202), (8,203), (9,202), (10,200)
Inserting these points into a calculator, the line of best fit is given as follows:
y = -1.62x + 215.64.
The estimate weight at the 15th week of the diet is the numeric value of the function when x = 15, that is, the lone instance of x in the function is replaced by 15, as follows:
y = -1.62(15) + 215.64 = 191.34 pounds.
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Find x in this equation.
3/8 = 15/5x - 2
Answer:
x=19/24
Step-by-step explanation:
3/8=15/5x-2
3/8= 3x -2 |*8
3=24x-16
24x=19
x=19/24
Warren likes to draw pictures of people and animals. In his notepad, he has drawn 2 pictures of people for every 5 pictures of animals.
If Warren has drawn 18 more pictures of animals than people in his notepad, how many pictures of animals has he drawn
By solving a linear equation, it is obtained that Warren has drawn 30 pictures of animals
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a linear equation needs to be solved
Let Warren has drawn 5x pictures of animals and 2x pictures of people
Warren has drawn 18 more pictures of animals than people in his notepad
By the problem,
5x - 2x = 18
3x = 18
x = [tex]\frac{18}{3}[/tex]
x = 6
Number of pictures of animals Warren has drawn = [tex]5 \times 6 = 30[/tex]
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When we add any two multiples of 5 and 10 we sometimes,always or never get a number ending in 2.
Sometimes
Never
Always
Answer:
Never
Because for example; 25(the multiple of 5) + 20(the multiple of 10) equals 45
Answer:
Step-by-step explanation:
never
A math class has a total of 33 students. The number of males is 15 more than the number of females. How many males and how many females are in the class?
During the WMS Presidential elections, candidate #1 received 75 votes whereas candidate #2, who
promised better lunches and longer seminar class times received 165 votes. What is the percentage
difference between the WMS Presidential Candidate # 1 and WMS Presidential Candidate # 2's total
number of votes?
Answer: candidate 2 has 90 votes
Step-by-step explanation:
165-75=90
A plumber who is just starting out offers low rates to attract new customers. He charges $35 to visit a client's home, plus an additional $20 per hour. If the plumber charges a customer $45 for a visit, how long was it?
If the plumber charges a customer $45 , then the visit was 0.5 hours long .
In the question ,
it is given that
the fixed charge to visit a client's home is = $35
additional per hour charge of plumber is = $20 .
let the time taken by plumber in the customer house be "x" .
So , according to the question
the equation for total charge is
total charge = 35 + 20x
given the customer paid $45 ,
So , 45 = 35 + 20x
20x = 45 - 35
20x = 10
x = 10/20 = 0.5
Therefore , If the plumber charges a customer $45 , then the visit was 0.5 hours long .
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David is three time as old as Joseph after 3 years David will be only twice as old as process will be there find their present ages
Answer:
Joseph's present age=3 yrs
David's present age=9 yrs
Step-by-step explanation:
Let Joseph's present age be x.
David's present age=3x
__________________
Ater 3 yrs,
Joseph's age=x+3
David's age=2(x+3)
Also, we can add 3 to David's present age to get age After 3 yrs. So, David's age after 3 yrs would also be 3x+3.
Now, balance them.
3x+3=2(x+3)
3x+3=2x+6
x=3
D"s prsent age=9
J's present age=3
2x-2y =-7 use elimination
Using elimination method in the equation 2x+y=7 and 2x*3y=3, x is 3 and y is 1.
Two equations are given solving it by using rule of elimination,
2x+y=7....(1) and 2x*3y=3. (2)
Multiply equation (1) by three to get 6x+3y=21. (3)
Add equations (2) and (3) together to get
8x=24
x=24/8
x= 3
Replace this number in equation (1):
2(3)+y=7
6+y=7
y=7-6
y= 1
Consequently, the answer is x=3,y=1.
To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
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On a banquet table, 8 different dishes of food will be placed in a row. There are 4 vegetarian dishes and 4 meat dishes.
They will be placed alternating between the two types of dishes. A vegetarian dish will be first. How many ways are
there to place the dishes on the table?
If a vegetarian dish will be first. The number of different ways that are there to place the dishes on the table is 576.
How to find the number of different ways?There are 4 vegetarian dishes = P4 = 4!
There are 4 meat dishes =P4 =4!
Now let find the number of different ways
Number of different ways = 4! × 4!
Number of different ways = 24 × 24
Number of different ways = 576 different ways
Therefore the number of different ways is 576.
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