Answer:
quotient-206
remainder-1
Step-by-step explanation:
Solve: 3.92 ÷ 0.07 (Answer as a decimal)
Answer:
56
Step-by-step explanation:
Answer:
0.56 or 56
Step-by-step explanation:
3.92/0.07 is 56 if you wanted to place it in decimal for you would have to move the decimal point 2 places over to get a decimal.
-4q-(-8q)+10 combine the like terms to create an equivalent expression
we have
-4q-(-8q)+10
step 1
Remove the parenthesis
-4q+8q+10
step 2
Combine like terms
4q+10
therefore
the answer is
4q+106. A company car purchased for $39,600 depreciates at 12% per annum. What is the car
worth after 3 years?
Answer:
$26,986.29
Step-by-step explanation:
We can use the formula for calculating the depreciation of an asset over time:
wor
\(\bold{D = P(1 - \frac{r}{100} )^t}\)
where:
D= the current value of the asset
P = the initial purchase price of the asset
r = the annual depreciation rate as a decimal
t = the number of years the asset has been in use
In this case, we have:
P = $39,600
r = 12% = 0.12
t = 3 years
Substituting these values into the formula, we get:
\(D= 39,600(1 - \frac{12}{100})^3\\D= 39,600(1 - 0.12)^3\\D= 39,600*0.88^3\\D= 39,600*0.681472\\D=26986.2912\)
Therefore, the car is worth approximately $26,986.29 after 3 years of depreciation at a rate of 12% per annum.
Answer:
$26,986.29
Step-by-step explanation:
As the car's value depreciates at a constant rate of 12% per annum, we can use the exponential decay formula to create a function for the value of the car f(t) after t years.
Exponential Decay formula\(\boxed{f(t)=a(1-r)^t}\)
where:
f(t) is the value of the car (in dollars) after t years.a is the initial value of the car.r is the depreciation rate (as a decimal).t is the time period (number of years after purchase).In this case, the initial value is $39,600, and the rate of depreciation is 12% per year. Therefore, the function that models the value of the car after t years is:
\(f(t)=39600(1-0.12)^t\)
\(f(t)=39600(0.88)^t\)
To calculate the value of the car after 3 years, substitute t = 3 into the function:
\(\begin{aligned} f(3)&=39600(0.88)^3\\&=39600(0.681472)\\&=26986.2912\\&=26986.29\;(\sf 2\;d.p.)\end{aligned}\)
Therefore, the car is worth $26,986.29 after 3 years.
Alan needs to mix 3 tablespoons of salt with 5 tablespoons of vinegar to make a cleaning solution. How many tablespoons of salt are needed for each tablespoon of vinegar? (5 points)
5 over 3 tablespoons
3 over 8 tablespoon
3 over 5 tablespoon
5 over 8 tablespoon
Answer:
I think it's C but I'm still thinking about this but it's C I think
Step-by-step explanation:
Put these numbers in order from least to greatest.
-1/4
2/40
-16
9/25
Answer:
(-1/4)(-16)(2/40)(9/25)Step-by-step explanation:
ax + by = 6 -2x + 4y = 12 In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a + b ?
Answer:
1
Step-by-step explanation:
You want the value of the sum a+b if the line ax+by=6 graphs the same as the line -2x +4y = 12.
Dependent EquationsThe equations describe the same line, so have infinite solutions, if the coefficients and constants are the same.
Here, we notice that the constant in the second equation (12) is double that in the first equation (6). We can make them the same by dividing the second equation by 2:
(-2x +4y)/2 = 12/2
-x +2y = 6
Since we want this to be the same line as ...
ax +by = 6
we must choose ...
a = -1b = 2SumThen the sum of the coefficients is ...
a + b = (-1) + (2) = 1
The value of a+b is 1.
There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?
Answer:
83 kids total
Step-by-step explanation:
There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?
girls = 54
boys = 54 - 25 = 29
54 + 29 = 83 kids total
kids that are on the playground are 83.
What is the sum?Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.
The total number of girls that are present is 54
The data given is that there are
25 fewer boys taht are4 present
The total number of boys will be
boys = 54 - 25 = 29
The number of kids that are present will be the total of boys and girls that are present.
Kids = boys + girls
54 + 29 = 83 kids total
The quantity of kids that are present in the playground is 83.
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Choose the best selection for the quadrilateral with vertices at the following points: (-2,0), (0,4), (4,0), (6,4) Hint: Start by graphing the points. Distance Formula: d= (x2 – x1)2 + (y2 – yı)? + B. Parallelogram a. Rectangle D. Trapezoid Rhombus
The best selection for the quadrilateral with the given vertices is: parallelogram.
Recall:
Parallel lines are lines do not intersect and they are equal distant apart.
The opposite side of a parallelogram are of equal length.
Thus, the points of the vertices of the quadrilateral has been graphed in the diagram shown below:
Point A (-2,0)
Point B (0,4)
Point C (6,4)
Point D (4,0)
Find the distance between each vertices using the distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Distance between Point A (-2,0) and Point B (0,4):
\(AB = \sqrt{(0 -(-2))^2 + (4 - 0)^2} \\\\\mathbf{AB = \sqrt{20} }\)
Distance between Point B (0,4) and Point C (6,4):
\(BC = \sqrt{(6 - 0)^2 + (4 - 4)^2} \\\\\mathbf{BC = 6 }\)
Using the same distance formula, CD = √20 while AD = 6
This means that the opposite sides of the quadrilateral with the given vertices are equal in length. Parallelogram has two pairs of equal sides.
Therefore, the best selection for the quadrilateral with the given vertices is: parallelogram.
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A manufacturing machine has two processes. One of them is repeated 4 times and the second only once. The entire cycle
can take no longer than 3 minutes. Which graph represents the overall equation represented by this scenario (all points
may not apply to the scenario)?
Answer:
The inequality representing the time taken by the entire cycle is:
\(4x+y\leq 3\)
Step-by-step explanation:
The time taken to complete one cycle of a manufacturing machine is no longer than 3 minutes.
It is provided that the manufacturing machine has two processes.
One of them is repeated 4 times and the second only once.
Assume that the variable x represents the time taken to complete the first process once.
Then the time taken to complete the first process 4 times would be, 4x.
Also assume that the variable y represents the time taken to complete the second process.
Then the inequality representing the time taken by the entire cycle is:
\(4x+y\leq 3\)
Consider the graph below representing the above equation.
Answer: D
Step-by-step explanation:
Simplify using order of operations.
Answer:
64 ÷ 16 = 4
Step-by-step explanation:
Using PEMDAS, you first do the parenthesis, which equals 64. Then you do the exponents, which 4² equals 16. Then you divide 64 by 16, which equals 4.
A triangle has sides that measure 5 units, 7 units, and 8 units. Is this a right triangle
will mark brainliest asap.
answer choices
Yes, it is a right triangle because 72 + 52 = 82.
No, it is not a right triangle because 72 + 52
≠
82.
Yes, it is a right triangle because 72 + 52
≠
82.
No, it is not a right triangle because 72 + 52 = 82.
Answer:
Step-by-step explanation:
O=0O
KO[K]
Solve the equation for y. 3x+y=7
Answer:
y = 7 - 3x
Step-by-step explanation:
3x + y = 7
Subtract 3x from both sides:
y = 7 - 3x
Answer:
y = 7 - 3x
Answer:
y = 7 - 3 x
Step-by-step explanation:
Solve for y:
y + 3 x = 7
Hint: | Solve for y.
Subtract 3 x from both sides:
Answer: y = 7 - 3 x
Solve the following for θ, in radians, where 0≤θ<2π.
−sin^2(θ)−2sin(θ)+1=0
Select all that apply:
0.75
2.5
2.71
0.95
0.43
2.04
The radian solutions of the equation are θ = 2.71 and θ = 0.43 radians
Finding all radian solutions of the equationFrom the question, we have the following parameters that can be used in our computation:
-sin² (θ) - 2sin (θ) + 1 = 0
Divide through by -1
So, we have
sin² (θ) + 2sin(θ) - 1 = 0
Let y = sin(θ)
So, we have
y² + 2y - 1 = 0
When solved graphically, we have
y = 0.414 and -2.414
This means that
sin(θ) = 0.414 and sin(θ) = -2.414
Take the arcsin of both sides
θ = 2.71 and θ = 0.43
Hence, the angles are θ = 2.71 and θ = 0.43
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Help me picture above
Answer:
Area of rectangle OABC = 18 units²
Step-by-step explanation:
From the graph attached,
Vertices of the rectangle are O(0, 0), C(3, 0) and A(0, 6).
Length of side AO = 6 units
Length of side OC = 3 units
Area of the rectangle = Length × Width
= OC × AO
= 3 × 6
= 18 square units
Help me please quickly
Answer:
the are of the triangle is 216
Step-by-step explanation:
3x9 is 27 27x8 is 216
A car was moving at 14 m/s. After 3 seconds, its speed increased to 20 m/s. What was the acceleration during this time?
Answer:
6 mph
Step-by-step explanation:
the cars acceleration was
6mph
PLEASE ANSWER ASAP! 25 POINTS!
Eric and his friends went to Burger King. They bought french fries and burgers for the movies. French fries cost $3 each, burgers cost $9 each. They spent a total of $102, and they bought a total of 16 items. Find out how many orders of french fries and burgers they bought.
Answer:
Burgers: 12
French Fries: 34
Step-by-step explanation:
Hello I need help please
Suppose that two motorboats leave the same point at the same time. If one travels north at 15 miles per hour and the other travels east at 20 miles per hour, how fast will the distance between them be changing after 2 hours? Draw a diagram to model the situation.
Answer:
I believe it would be 70 miles between them.
Which of the following statements is not true?
Choose the incorrect statement below.
The three-part inequality - 1 <-3x ≤ 1 is equivalent to -5x<
15x2
<3 is equivalent to -6≤5-x<6.
The three-part inequality - 3s-
OD. The three-part inequality -7≤11-x<7 is equivalent to 4 < x≤ 18.
OA.
OB.
C.
The three-part inequality -5s-10x<5 is equivalent to
5-x
...
The incorrect statement is:
B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.
In the given statement, there is an error in the inequality. The correct statement should be:
The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.
When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:
- 5x < 15x^2 and 15x^2 < 3
Simplifying the first inequality:
- 5x < 15x^2
Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:
- 5 < 15x
Simplifying the second inequality:
15x^2 < 3
Dividing by 15, we get:
x^2 < 1/5
Taking the square root (assuming x ≥ 0), we have two cases:
x < 1/√5 and -x < 1/√5
Combining these inequalities, we get:
- 5 < 15x and x < 1/√5 and -x < 1/√5
Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.
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Enter the ratio as a fraction in lowest terms.
5 ft to 70 in.
Answer:
1/14
Step-by-step explanation:
The ratio is 5:70. The fraction form of that is 5/70. To get the lowest terms, I divided both numbers by 5. So it is 1/14
You are washing cars over the summer. It costs you $3 to wash each car and a one-time cost of $35 for some supplies to market your car wash. You plan to charge $10 per wash. Write an equation and solve to determine the amount of cars you need to break even.
The amount of cars you need to break even is 5.
To determine the number of cars you need to break even, we can set up an equation where the revenue equals the total cost.
Let's denote the number of cars as x.
Revenue = Number of cars × Price per wash
= x × $10
Total cost = Cost per car × Number of cars + One-time cost
= $3x + $35
To break even, the revenue should be equal to the total cost:
x × $10 = $3x + $35
Now, let's solve this equation to find the value of x:
10x = 3x + 35
Subtract 3x from both sides:
10x - 3x = 3x + 35 - 3x
7x = 35
Divide both sides by 7:
x = 35 / 7
x = 5
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if x=3, what is Y?
x= -3,0,3,6
y= -5,-4,-3,-2
Answer:
If x = 3, then y = -2 since the corresponding value of y for x=3 is -2 in the given table.
Step-by-step explanation:
PRE CALC HELP NEEDED
Answer:
\(\dfrac{5e^2}{2}\)
Step-by-step explanation:
Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.
Given function:
\(y=x^2\ln(2x)\)
Differentiate the given function using the product rule.
\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)
\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)
\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)
Input the values into the product rule to differentiate the function:
\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)
To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:
\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)
Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:
\(\boxed{\dfrac{5e^2}{2}}\)
Write the equation 10x + 5y = 5 in slope-intercept form
(2 Points)
The images below show a picture of ricoffy tin container with no dimensions indicated.the container is 2,5 times smaller than what it is in reality. Measure the diameter of the tin in mm and write down the real diameter in mm
The diameter of the tin in the picture is \(3d/5\) where 'd' is the diameter of the tin in reality.
What is the measurement of the diameter?Determining the diameter of tin:
Since there is no indication of dimensions, represent the diameter with a variable 'd' and find the diameter of the tin according to the given condition in the problem.
Here we have assumed that the diameter of the tin is 'd' in reality and the diameter of the tin picture can be calculated as given below.
Here we have
A ricoffy tin container with no dimensions indicated
Let d and h be the diameter and height of the tin
Given that the container is 2/5 times smaller than d
then the diameter of the tin in the picture \(= d - 2/5(d)\)
\(= [5d - 2d]/5 = 3d/5\)
Therefore, The diameter of the tin in the picture is \(3d/5\) where 'd' is the diameter of the tin in reality.
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-3(-7b + 3) + 8b = 5b-4(1 - 6b)
Answer:
No solution
Step-by-step explanation:
If a polynomial function f(x) has roots –8, 1, and 6i, what must also be a root of f(x)?
Answer: -6i
Step-by-step explanation:
6)Paul has a coupon at the Guitar Store for 15% off any purchase of $100 or more.
He wants to buy a used guitar that has a price tag of $220 on it. Paul wonders how
much money the coupon will take off of the $220 original price.
a. $15
b. $30
C. $33
d. $66
e. None of above. EXPLAIN!
Hi I need help with this geometry calculus 1 problem. I’m in high school and this is a homework. thank you!
Analysis on Perimeter
The shape is made up of a semicircle and a rectangle.
The perimeter of a semicircle is calculated using the formula:
\(P_C=\pi r\)From the image, the diameter of the rectangle is given to be x. Since we know that the diameter is twice the length of the radius, this means that:
\(r=\frac{d}{2}=\frac{x}{2}\)Hence, the perimeter of the semicircle in terms of x becomes:
\(P_C=\frac{\pi}{2}x\)The perimeter of a rectangle is given to be:
\(P_R=2l+2w\)Already, we have the base length to be x, therefore:
\(w=x\)Note, though, that the connecting sides between the semicircle and the rectangle are not included in the perimeter length given. Therefore, the perimeter of the rectangle will be:
\(\begin{gathered} P_R=2l+w \\ P_R=2l+x \end{gathered}\)Since the perimeter is given to be 40 feet, then we have:
\(\begin{gathered} P_R+P_C=40 \\ \therefore \\ 2l+x+\frac{\pi}{2}x=40 \end{gathered}\)We can get the length of the rectangle by making l the subject of the formula:
\(\begin{gathered} 2l=40-x-\frac{\pi}{2}x \\ \text{Dividing through by 2, we have:} \\ l=\frac{40}{2}-\frac{x}{2}-\frac{\pi}{2\times2}x \\ l=20-\frac{x}{2}-\frac{\pi}{4}x \end{gathered}\)Combining to a single fraction, we have:
\(l=\frac{80-2x-\pi x}{4}\)AREA OF THE WINDOW
The area of the window can be gotten by using the formula:
\(A=A_C+A_R\)The area of a semicircle is gotten using the formula:
\(A_C=\frac{\pi r^2}{2}\)Therefore, the area will be:
\(\begin{gathered} A_C=\frac{\pi(\frac{x}{2})^2}{2}=\frac{\pi x^2}{2\times4} \\ A_C=\frac{\pi x^2}{8} \end{gathered}\)The area of the rectangle will be:
\(A_R=l\times w\)Inputting our known values, we have:
\(\begin{gathered} A_R=\frac{80-2x-\pi x}{4}\times x \\ A_R=x(\frac{80-2x-\pi x}{4}) \end{gathered}\)Therefore, the combined area will be:
\(A=\frac{\pi x^2}{8}+x(\frac{80-2x-\pi x}{4})\)Combining the fraction, we have:
\(A=\frac{\pi x^2+2x(80-2x-\pi x)}{8}\)Expanding the bracket, we have:
\(A=\frac{\pi x^2+160x-4x^2-2\pi x^2}{8}=\frac{160x-4x^2-\pi x^2}{8}\)Therefore, the function of the area is:
\(A=\frac{160x-4x^2-\pi x^2}{8}\)The owner of an apartment building can rent all 50 apartments if she charges $600 per month, but she rents one fewer apartment for each $20 increase in monthly rent. Identify the maximum revenue for this function?
Answer:
30,000
Step-by-step explanation:
If she gets all 50 at 600 per month, 50x600 is 30,000.
I hope this helped!