The sales tax in Bill's state is 6%. Bill bought a Scion having a sales tax of $820. What was the cost of the car, rounded to the nearest dollar.
Mick and LaToya have some shirts. The ratio of the number of shirts Mick has to the number of shirts LaToya has is 3:8. If they have a total of "k" shirts, how many fewer shirts does Mick have than LaToya?
With the beam being held still at a height of 40 m, the crane breaks and the beam falls to the ground. Assuming no air resistance, how much total energy will the beam have just as it hits the ground?
The total energy of the beam just as it hits the ground would be equivalent to the initial potential energy when it was held at a height of 40 m, assuming no air resistance.
Explanation:The question is about understanding the concept of conservation of energy, specifically the transformation of potential energy to kinetic energy. When the beam was held at a height of 40 m, it had potential energy given by the formula:
PE = mgh
where m is the mass of the beam, g is the acceleration due to gravity, and h is the height. Assuming no air resistance, when the beam falls, all of its potential energy will be converted to kinetic energy, which can be determined by the formula:
KE = 1/2 mv^2
However, as we don't know the exact speed of the beam just as it's hitting the ground, we don't need it because the total energy remains constant. So, just as the beam hits the ground the total energy will be the same as the initial potential energy when it was still.
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A total of 487 tickets were sold for the school play. They were either adult tickets or student tickets. There were 63 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Final answer:
To determine the number of adult tickets sold for the school play, a system of equations is set up and solved, revealing that 275 adult tickets were sold.
Explanation:
To find the number of adult tickets sold for the school play, we need to set up a system of equations based on the information given. Let x represent the number of adult tickets and y represent the number of student tickets. According to the problem, the following two statements are true:
The total number of tickets sold is 487: x + y = 487
There were 63 fewer student tickets sold than adult tickets: y = x - 63
We can substitute the second equation into the first to find the value of x:
x + (x - 63) = 487
2x - 63 = 487
2x = 487 + 63
2x = 550
x = 275
Therefore, 275 adult tickets were sold.
Suppose Q and R are independent events. Find P(Q and R) if P(Q) =4/5 and P(R) =4/11
A chemist is using 353 millimeters of a solution of acid and water. If 16.5% of the solution is acid, how many millimeters of acid are there? Round your answer to the nearest tenth.
Find the arc length of the curve on the given interval. (round your answer to three decimal places.) parametric equations interval x = 6t + 5, y = 7 − 7t −1 ≤ t ≤ 3
The arc length of the curve on the given interval −1 ≤ t ≤ 3 with parametric equation x = 6t + 5 and y = 7 − 7t −1 is 4√85.
What is integration?It is the reverse of differentiation.
The arc length of the curve on the given interval.
Parametric equations interval
x = 6t + 5, −1 ≤ t ≤ 3
y = 7 − 7t, −1 ≤ t ≤ 3
We know that the parametric form of the arc length will be given as
[tex]\rm \int _{-1}^3 \sqrt{(\dfrac{dx}{dt})^2 + (\dfrac{dy}{dt})^2} \ dt[/tex]
Then we have
[tex]\rm \dfrac{dx}{dt} = 6\\\\\dfrac{dy}{dt} = -7[/tex]
Then the arc length will be
[tex]\rightarrow \rm \int _{-1}^3 \sqrt{(3)^2 + (-7)^2} \ dt\\\\\rightarrow \sqrt{85} [t]_{-1}^3 \\\\\rightarrow 4 \sqrt{85}[/tex]
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What is the arc measure of an arc with length 4.189 cm and radius equal to 3 cm.'?
A company that creates model cars uses a 1.5 foot : 1 inch ration when creating the models. If a real car is 12 feet long, how long will the model car be?
Tina wants to save money for school. Tina invests 400$ in an account that pays interest rate of 8%. How many years will it take if her goal is 5500$
How Do You Sell More Walnuts In A Perfectly Competitive Market?
If the equilibrium price in a perfectly competitive market for walnuts
is $4.99 per pound,then an individual firm in this market can
A. Not sell additional walnuts unless the firm lowers its price.
B. Not sell additional walnuts at any price because the market is at equilibrium.
C. Sell an additional pound of walnuts at $4.99.
D. Sell more only by increasing its advertising budget.
the subject is Economics.
In the middle of the page draw a equilateral triangle with 2 inch sides and the bottom parallel to the of the page
The sum of the angle of a triangle is 180 degrees. If you are to draw a pattern of equilateral triangles then you know that an equilateral triangle has three equal sides. Also, its angles are the same, having 60 degrees at each corner of the triangle. A triangle cannot qualify as an equilateral triangle if it is greater than 180 degrees or less than 180 degrees as a total angle. Also if a triangle that has no two right angles, then it is called a scalene triangle. If the triangle has two right angles, it is called isosceles triangle. A triangle with equal sides is called an equilateral triangle.
A company made 4 million in the second quarter this is 1/3 more then it made in the first quarter and 4/5 of what it made in the third quarter how much did the company make in all 3/4 combined
A total of 504 tickets were sold for the school play. They were either adult tickets or student tickets. There were 54 more student tickets sold than adult tickets. How many adult tickets were sold?
Using algebra, we find that 225 adult tickets were sold out of a total of 504 tickets.
Explanation:Let's denote the number of adult tickets as x. Since there were 54 more student tickets sold than adult tickets, we can represent the number of student tickets as x + 54. The total number of tickets sold is 504, so we set up the equation x + (x + 54) = 504.
Combining like terms, we get 2x + 54 = 504. Subtracting 54 from both sides gives us 2x = 450. Finally, dividing both sides by 2 gives us x = 225.
Therefore, 225 adult tickets were sold.
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Sara must plant 340 trees. In the past 6 days Sara planted 204 trees. If she continues at this rate, how many more days will it take her to plant all the trees?
which number produces a rational number when added to 0.5
Answer:
Any rational number.
Step-by-step explanation:
∴ [tex]x+0.5[/tex] is rational if and only if x is rational.
To proveL: we proceed as follows:
Suppose that [tex]x+0.5[/tex] is rational.
Then there are some integers p , q with [tex]q\neq 0[/tex] such that
[tex]x+\frac{1}{2}=\frac{p}{q}[/tex]
Subtract both sides by [tex]\frac{1}{2}[/tex], we get
[tex]x=\frac{p}{q}-\frac{1}{2}=\frac{2p-q}{2q}[/tex] which is rational.
Conversely, if x is rational, then there are integers a,b with b>0 such that [tex]x=\frac{a}{b}[/tex] then we have,
[tex]x+\frac{1}{2}=\frac{a}{b}+\frac{1}{2}=\frac{2a+b}{2b}[/tex] which is also a rational.
What's the average of 200 and 300
domain and range of x^2+x-2/x^2-3x-4
Write this number in standard form. 12 ten thousands, 8 thousands, 14 hundreds and 7 ones
What is the slope of a line that passes through the following points (-3,8) and (2,1)
Hello!
Step-by-step explanation:
Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]
[tex]\frac{1-8=-7}{2-(-3)=2+3=5}=\frac{-7}{5}=-\frac{7}{5}[/tex]
Slope is -7/5
Answer is -7/5
Hope this helps!
Thanks!
-Charlie
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a patient requires 30% decrease in the dosage of the medication her current dosage is 340 MGS what will the dosage be after the decrease
Answer:
The dosage will be 238 MGS after decrease.
Step-by-step explanation:
The current dosage of the medication of the patient = 340 MGS
patient requires 30% decrease in the dosage of the medication.
Now her new dosage after decrease = 340 -(30% × 340)
= 340 -(0.30 × 340)
= 340 - 102
= 238 MGS
The dosage will be 238 MGS after decrease.
A bird feeder is in the shape of a cylinder. It has a volume of about 100 cubic inches. It has a radius of 2 inches. What is the approximate height of the bird feeder? Use 3.14 for pi
volume = pi x r^2x h
100 = 3.14 x 2^2 x h
100 =3.14 x 4 x h
100 = 12.56 x h
h = 100/12.56 = 7.9617
the height is approximately 8 inches tall
What is the volume of an oblique cone with radius 9 cm and height 12 cm?
972π cm3
486π cm3
648π cm3
324π cm3
Find an approximation of the area of the region R under the graph of the function f on the interval [-1, 2]. Use n = 6 subintervals. Choose the representative points to be the left endpoints of the subintervals. f(x) = 7 - x2
The approximation of the area of the region R under the graph of the function is 18.625 square units.
In this question we must calculate the approximate area ([tex]A[/tex]) below the curve by means of Riemann sums with left endpoints, whose expression is described below:
[tex]A = \Delta x \cdot \Sigma\limits^{n-1}_{i=0} f(a + i\cdot \Delta x)[/tex], for [tex]x \in [a,b][/tex] (1)
[tex]\Delta x = \frac{b-a}{n}[/tex] (2)
Where:
[tex]a[/tex] - Lower bound[tex]b[/tex] - Upper bound[tex]n[/tex] - Number of subintervals[tex]i[/tex] - IndexIf we know that [tex]a = -1[/tex], [tex]b = 2[/tex], [tex]n = 6[/tex] and [tex]f(x) = 7 - x^{2}[/tex], then the approximate area is:
[tex]\Delta x = \frac{2-(-1)}{6}[/tex]
[tex]\Delta x = 0.5[/tex]
[tex]A = 0.5\cdot [f(-1) + f(-0.5)+f(0)+f(0.5)+f(1)+f(1.5)][/tex]
[tex]A = 0.5\cdot (6+6.75+7+6.75+6+4.75)[/tex]
[tex]A = 18.625[/tex]
The approximation of the area of the region R under the graph of the function is 18.625 square units.
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Bill's Roast Beef sells 5 times as many sandwiches as Pete's Deli. The difference between their sales is 360 sandwiches. How Many did each sell ?
Answer:
5y-y =360
4y =360
y= 90 sandwiches by Pete's deli
x= 5(90) = 450 sandwiches by Bills Roast Beef
Step-by-step explanation:
A cold front moved in last weekend. In eight hours overnight, the temperature outside dropped from 14 degrees to -10. What was the average temperature change for each hour ?
A figure has a vertex at (5, 2). If the figure has line symmetry about the y-axis, what are the coordinates of another vertex of the figure?
Answer:
[tex](-5,2)[/tex]
Step-by-step explanation:
We have been given that a figure has a vertex at (5,2). The figure has line symmetry about the y-axis.
We know that if a figure is symmetric about y-axis, then its x-coordinate changes to opposite sign and y-coordinate remains same.
We can see that x-coordinate of our given point is 5, so x-coordinate of another vertex of the figure would be -5.
Therefore, the point [tex](-5,2)[/tex] is symmetric about y-axis for our given point.
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In how many different ways can you make exactly 0.75 using only nickles dimes and quarters if you have at least one of each coin?
5. Simplify (15x2 – 24x + 9) ÷ (3x – 3) = ?