Your friend has $100 when he goes to the fair. He spends $10 to enter the fair and $20 on food. Rides at the fair cost $2.00 per ride. Which function can be used to determine how much money he has left over after x rides?
Marta processed and shipped 424 orders last year. She polled 128 of her customers, 99 of whom replied that they were completely satisfied with their orders.
To the nearest whole percent, the estimated population proportion of the customers who were completely satisfied was ___%
Answer:
77%
Step-by-step explanation:
what is the inverse of the function below
Answer:
[tex]f^{-1}=4(x+2)[/tex]
Step-by-step explanation:
[tex]f(x)=\frac{x}{4} -2[/tex]
To find inverse function , replace f(x) with y
[tex]y=\frac{x}{4} -2[/tex]
Swap the variables x and y
[tex]x=\frac{y}{4} -2[/tex], nbw we solve for y
Add 2 on both sides
[tex]x+2=\frac{y}{4}[/tex]
Now to eliminate 4, we multiply 4 on both sides
[tex]y=4(x+2)[/tex]
Replace y with f^-1
[tex]f^{-1}=4(x+2)[/tex]
One side of a right triangle is known to be 9 cm long and the opposite angle is measured as 30°, with a possible error of ±1°. (a) use differentials to estimate the error in computing the length of the hypotenuse. (round your answer to two decimal places.)
To estimate the error in the hypotenuse length of a right triangle using differentials, we use the trigonometric identity sin(θ) = opposite/hypotenuse, finding the derivative, and then apply the angle error to get an error estimate of
±0.31 cm in the hypotenuse length.
The question asks to use differentials to estimate the error in computing the length of the hypotenuse of a right triangle when one side is 9 cm and the opposite angle is 30° with a possible error of ±1°. To calculate the hypotenuse (c) when dealing with problems involving right triangles, you can use the trigonometric identity sin(θ) = opposite/hypotenuse, which can be rearranged to c = opposite/sin(θ). The differential of c with respect to θ is dc/dθ = -opposite * cos(θ)/sin2(θ). Given that the opposite side is 9 cm and the angle θ is 30°, we can find dc/dθ and then multiply by the possible angle error of ±1° to estimate the error in the hypotenuse length.
Plugging in the given values and converting the angle to radians (since the derivative is taken with respect to radians), we find
dc/dθ ≈ -9 cm × cos(30°)/sin2(30°) ≈ -18 cm.
The possible change in angle is ±1°, which in radians is approximately ±0.0175 radians, thus
Estimated error in hypotenuse ≈ -18 cm × ±0.0175 ≈ ±0.315 cm.
Therefore, the estimated error in the length of the hypotenuse, rounded to two decimal places, is ±0.31 cm.
Need help with this been trying to solve it
x/3ytimes3xy/5dividedby4y^2/5x^2
Fractions,
PLEASE HELP
Hour truck can carry a 3/4 ton load. Each brick weighs 4 lbs and 14 oz. How many bricks can the truck carry
Consider the solid shaped like an ice cream cone that is bounded by the functions z=x2+y2‾‾‾‾‾‾‾√ and z=50−x2−y2‾‾‾‾‾‾‾‾‾‾‾‾√. set up an integral in polar coordinates to find the volume of this ice cream cone.
To calculate the volume of a solid bounded by two functions, set up an integral in polar coordinates. The volume is found by integrating the difference of the two volumes described by the functions (50 - sqrt(x²+y²) - sqrt(x²+y²)) over r, θ, and z within their appropriate limits.
Explanation:The subject of the question is mathematics, more specifically, integral calculus in spherical or polar coordinates. Calculating the volume of a solid bounded by two functions can be done by taking the difference of the two function volumes.
The integrals, using polar coordinates (r and θ), are set up as follows:
Volume = ∫∫∫(50 - sqrt(x²+y²) - sqrt(x²+y²)) r dr dθ dz,
where the limits for r are [0, sqrt(50)], for θ are [0, 2π], and for z are [0, 50]. Also, note that 'x²+y²' is replaced with 'r²' because in polar coordinates, 'r' represents the square root of x^2 plus y^2.
This integral, when solved, gives the volume of the ice cream cone-shaped solid.
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The volume of the ice cream shaped solid can be found by converting the limits of the cone to polar coordinates and performing a double integral. The limits of the cone are represented by the expressions z = r and z = sqrt(50 - r^2). The volume integral will be ∫ _(theta=0 to 2*pi) ∫ _(r=0 to sqrt(50)) [(sqrt(50 - r^2)) - r] r dr dθ.
Explanation:To evaluate the volume of the solid resembling an ice cream cone, we can use the method of double integration in polar coordinates. Because we're dealing with a cone, polar coordinates are suitable as they're related to circular symmetry.
The limits of the cone are given by the functions z = sqrt(x^2 + y^2) and z = sqrt(50 - x^2 - y^2). In polar coordinates these become z = r and z = sqrt(50 - r^2).
To evaluate the volume of the cone, we need to subtract the volume of the lower cone (given by z = r) from the volume of the upper cone (given by z = sqrt(50 - r^2)). We convert the values to polar coordinates and use double integration as follows:
V = ∫ _(theta=0 to 2*pi) ∫ _(r=0 to sqrt(50)) [(sqrt(50 - r^2)) - r] r dr dθ
This integral, once solved, will give the volume of the ice cream shaped solid.
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Find all the second partial derivatives. v = e5xey
Final answer:
The second partial derivatives of v = e⁵x * ey are ∂²v/∂x² = 25e⁵x * ey and ∂²v/∂x² = 5e⁵x * e^y.
Explanation:
To find the second partial derivatives of the function v = e⁵x * ey, we need to differentiate twice with respect to x and y. Let's start with the first partial derivative with respect to x:
∂v/∂x = ∂(e⁵x * ey)/∂x
= 5e⁵x * ey
Next, we differentiate the first partial derivative with respect to x to find the second partial derivative with respect to x:
∂²v/∂x² = ∂(5e⁵x * ey)/∂x
= 25e⁵x * ey
Similarly, the second partial derivative with respect to y is:
∂²v/∂x² = ∂(5e⁵x * ey)/∂y
= 5e⁵x * e^y
there are 36 female preformers in a dance recital.the ratio of men to women is 2:9 how many men are in the dance recital.
2:9 means for every 2 men there are 9 women
36/9 =4
4*2 = 8
there are 8 men
Solve -2 (x+5)=1/4(x-10)
Spence Ferris, a sales representative, drove 4 1/2 hours on the first day of his business trip, 8 3/4 hours on the second day, 6 2/3 hours on the third day, and 5 1/6 hours on the fourth day. If he must drive a total of 30 hours in five days, how much hours must Spence drive on the fifth day.
3(4x + 3) = 2x - 5(3 - x) + 2
The solution to the given-equation represented by "3(4x + 6) = 9x + 12" is : (b) x = -2.
To find the solution to the equation 3(4x + 6) = 9x + 12, we simplify and solve for x,
First, we distribute the 3 to both terms,
12x + 18 = 9x + 12
Next, we separate variable-term by subtracting 9x from both sides:
12x - 9x + 18 = 9x - 9x + 12,
Simplifying further:
We get,
3x + 18 = 12,
Next, we separate "x" by subtracting 18 from both sides,
3x + 18 - 18 = 12 - 18,
3x = -6,
(3x) / 3 = (-6) / 3,
x = -2
Therefore, the correct answer is (b) x = -2.
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The given question is incomplete, the complete question is
What is the solution to the equation 3(4x + 6) = 9x + 12?
(a) x = 2,
(b) x = -2,
(c) x = 10,
(d) x = -10.
Is (-2,5) a solution to the inequality y<-3x+4 show steps
What is the equation of the line tangent to the curve xy=4 at (2,2)?
If one million people have equal chances of being called by telephone from a broadcasting show, then the probability of one particular person receiving that call is .
Makayla's local movie theater has a moviegoer club that charges an annual registration fee of 25 dollars.However, movie tickets are discounted for members at 6 dollars per ticket, instead of 9 dollars per ticket.Let m equal the number of movie tickets Makayla purchases in a year. Write a function to model the amount of money Makayla spent going too the movies during the year she joined the club. C(m)=6x+25 The domain is best represented by: A)integers B)whole numbers C)rational numbers D)real numbers Algebra chestercat
Sue uses the expression ( 8 x 3,000) + ( 8 x 200) + (8 x 9) to help solve a multiplucation problem what is Sue's multiplucation problem?
Answer:
Sues problem would be - 8×3,209 :8×3,209
If 0.5 lb of Starbucks Coffee costs $6.48, what is the unit price for Starbucks Coffee? Hint: this involves decimal division.
The unit price of Starbucks Coffee, when 0.5 lb costs $6.48, is calculated by dividing the total cost by the pounds, resulting in $12.96 per pound.
Explanation:If 0.5 lb of Starbucks Coffee costs $6.48, to find the unit price for Starbucks Coffee, we perform a simple division. You want to know how much 1 lb would cost, given that 0.5 lb costs $6.48. To do this, you divide the total cost by the number of pounds.
$6.48 ÷ 0.5 = $12.96 per pound
This means that the unit price of Starbucks Coffee, when given a price of $6.48 for a half-pound, is $12.96 per pound. This calculation is crucial in understanding how to break down costs into more manageable, standard units, making price comparisons easier and more straightforward.
Jacob, Kylie, and Manuel each bought a sandwich and drink. The total bill to $21, and each drink cost $2. Of each sandwich cost the same amount, what is the cost of one sandwich?
Approximate to pi 13.0909091
The radius of a circle is increasing at a rate of 3 cm per minute. find the rate of change of the area when
Help please!! 20 points and brainliest!!
solve the system of linear equations. separate the x- and y- values with a coma. -9x+6y=-30
-12x+9y=-30
The sum of three numbers is 142. The first number is 8 less than the second. The third number is 4 times the second. What are the numbers?
In a biology lab, a student has measured the lengths of 30 palmetto bugs in inches. he computes the mean and standard deviation as 4.1 inches and 1.2 inches, respectively. he later finds out that he was supposed to calculate the mean and standard deviation in centimeters instead of in inches. what is the new standard deviation of his sample, in centimeters? (note: 1 in = 2.54 cm)
A coral reef grows 0.13m every week. How much does it grow in 9 weeks?
What is the value of the expression
–180
–5
5
24
how many liters of a 20% acid solution must be mixed with a 50% acid solution to obtain 12 liter of a 30% solution?
A large dinosaur was 89 feet long. Convert the length to meters. (Use 1 yd≈0.9144 m.)
An electrician has 4.1 meters of wire. How many strips 7/10 meters long can he cut?
Two triangles have side lengths 3, 4, 5 and 6, 8, 10, respectively. The triangles are similar to each other.
The missing side length of the second triangle is 8.
To find the missing side length of the second triangle, we can use the property that similar triangles have proportional side lengths.
Given:
First triangle: ( 3, 4, 5 )
Second triangle: ( 6, x, 10 )
Since the triangles are similar, the ratios of corresponding sides are equal:
[tex]\[ \frac{6}{3} = \frac{x}{4} = \frac{10}{5} \][/tex]
From the first ratio, [tex]\( \frac{6}{3} = \frac{x}{4} \)[/tex], cross multiply:
[tex]\[ 6 \times 4 = 3 \times x \][/tex]
[tex]\[ 24 = 3x \][/tex]
Divide both sides by 3 to solve for ( x ):
[tex]\[ x = \frac{24}{3} \][/tex]
[tex]\[ x = 8 \][/tex]
So, the missing side length of the second triangle is 8.
Here's a detailed calculation step-by-step:
1. Set up the ratios of corresponding sides: [tex]\( \frac{6}{3} = \frac{x}{4} = \frac{10}{5} \).[/tex]
2. Use the first ratio to find [tex]\( x \): \( 6 \times 4 = 3 \times x \)[/tex].
3. Solve for [tex]\( x \): \( 24 = 3x \)[/tex].
4. Divide both sides by 3: [tex]\( x = \frac{24}{3} = 8 \)[/tex].
5. Therefore, the missing side length of the second triangle is 8.
Complete Question:
Two triangles have side lengths 3, 4, 5 and 6, _____, 10, respectively. The triangles are similar to each other. Find the missing side of the triangle.