Answer:
Option A - 0.5 pounds
Step-by-step explanation:
Given : Beatriz determined the margin of error as 23.5 pounds to 24.5 pounds.
To find : What was the greatest possible error for her actual measurement?
Solution :
To find the margin of error first we find the median of the given numbers.
Median of 23.5 and 24.5
[tex]M=\frac{23.5+24.5}{2}=\frac{48}{2}=24[/tex]
So, the Greatest possible error is 24.5-24 = 0.5 pounds
Therefore, option A is correct.
a chord of length 24cm is 13cm from the centre of the circle. caculate the radius of the circle
what is the exact volume of this cylinder? 4in 8in
The volume of the cylinder is; 128π in3
Base area(πr^2)*height
Π = 3.14
Therefore; 3.14 * 4^2 * 8
3.14 * 128
= 401.92 in3
what dose a right angle look like ?
(A) A bag of trail mix weighs 2 lb. By weight, 20% of the bag is oats. How many pounds is the oats portion of the trail mix? Write an equation for the situation and label the “part,” “whole,” and “percent.”
(B) What is the weight of the oats in the trail mix? Show your work!
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The trapezoid below has an area of 1575 cm. What equation could you solve to find the height of the trapezoid
Answer:
A
Step-by-step explanation:
What are the solutions of the equation x4 + 95x2 – 500 = 0?
Answer:
C
Step-by-step explanation:
x = plus-or-minus StartRoot 5 EndRoot and x = ±10i
ED 2021
The room measures 8 inches by 5 inches on the blueprint. If the scale on the blueprint is 1 inch by 4 feet, what is the actual area of the room
The function h(t) = -2 (t-3)^2 +23 represents the height in feet, t seconds after a volleyball is served which of the following statements are correct
A. the volleyball reached it's maximum height of 3 sec
B. The maximum height of the vollybal was 23 ft
C. If the vball is not returned by the opposing team it will hit the ground in 5.5 sec
D. The graph that models the volleyball height over time is exponential
E. The vball was served from a height of 5 ft
Answer:
A. the volleyball reached it's maximum height of 3 sec
B. The maximum height of the vollybal was 23 ft
E. The vball was served from a height of 5 ft
Step-by-step explanation:
h(t) = -2 (t-3)^2 +23
Given equation is in the form of [tex]f(x)= a(x-h)^2 + k[/tex]
(h,k) is the vertex
Now we compare f(x) with h(t)
h(t) = -2 (t-3)^2 +23
h = 3 and k = 23
Vertex is (3,23)
h=3 . this means the volleyball reaches its maximum height in 3 seconds
k = 23. this means the volleyball reaches the maximum height of 23 ft
When ball reaches the ground the height becomes 0. so plug in 0 for h(t) and solve for t
0= -2 (t-3)^2 +23
Subtract 23 on both sides
-23 = -2(t-3)^2
Divide both sides by -2
[tex]\frac{-23}{-2} = (t-3)^2[/tex]
Take square root on both sides
[tex]+-\sqrt{\frac{23}{2}}= t-3[/tex]
Add 3 on both sides
[tex]+-\sqrt{\frac{23}{2}}+3= t[/tex]
We will get two value for t
t=-0.39 and t= 6.39
So option C is not correct
Given h(t) is a quadratic function not exponential
To find initial height we plug in 0 for x and find out h(0)
h(0) = -2 (0-3)^2 +23 = -2(-3)^2 + 23= -18+ 23= 5
The volleyball was served from a height of 5 ft
what does it mean by what is the name of the angle pairs formed by angle b and angle a?
Angle a and angle b are pairs of angles called the alternate angles. Alternate angles are pair of angles that is formed by two parallel lines. These two angles are not adjacent to each other. They are located on the opposite sides of the line that intersects the parallel lines.
Some one help me with this question!
One of the halves on the Hoover Dam releases 40,000 gallons of water per second. What is the rate, in gallons per minute?
Fill in the table and guess the value of the limit: \lim\limits_{x \to 3} f(x), where f(x)= \frac {x^3 - 27} {x^2 - 9}
Final answer:
To find the limit of f(x) as x approaches 3, factor the numerator and denominator as differences of squares, cancel common terms, and substitute x = 3 into the simplified fraction to get the limit, which is 4.5.
Explanation:
The student's schoolwork question involves calculating the limit of a function as x approaches a certain value. Specifically, the function in question is f(x) = (x^3 - 27) / (x^2 - 9) and the limit to be computed is limx → 3 f(x). To solve this, first recognize that directly substituting x = 3 would result in a 0/0 indeterminate form. To find the limit, we'll use algebraic manipulation.
Since both the numerator and the denominator are differences of squares, factoring them would give (x-3)(x^2+3x+9) for the numerator and (x-3)(x+3) for the denominator. The x-3 terms cancel out, leaving us with x^2+3x+9 over x+3. Now, substituting x = 3 into the simplified fraction will provide the value of the limit.
Calculating the limit step by step:
Original function: f(x) = (x^3 - 27) / (x^2 - 9)
Factor both numerator and denominator: f(x) = [(x-3)(x^2+3x+9)] / [(x-3)(x+3)]
Cancel out (x-3) terms: f(x) = (x^2+3x+9) / (x+3)
Substitute x = 3: f(3) = (3^2+3*3+9) / (3+3) = (9+9+9) / 6 = 27 / 6 = 4.5
Write the following decimal number in its equivalent fraction form. Show all work for full credit.
0.8(repeating)
To write the decimal number 0.8(repeating) as a fraction, use the concept of an infinite geometric series and convert it to an equation. Multiply both sides of the equation by 10 to eliminate the decimal point and subtract the original equation to eliminate the repeating part. Finally, divide by 9 to get the equivalent fraction form.
Explanation:To write the decimal number 0.8(repeating) as a fraction, we can use the concept of an infinite geometric series. Let's assume the repeating decimal as x: x = 0.8(repeating). Now, multiply both sides of the equation by 10 to remove the decimal point: 10x = 8(repeating). Next, subtract the original equation from this new equation to eliminate the repeating part: 10x - x = 8(repeating) - 0.8(repeating). Simplifying these expressions gives us: 9x = 7.2. Finally, divide both sides of the equation by 9: x = 7.2/9. Therefore, the equivalent fraction form of 0.8(repeating) is 7.2/9.
In a lot (collection) of 100 light bulbs, there are 5 defective bulbs. an inspector inspects 10 bulbs selected at random. find the probability of finding at least one defec- tive bulb. hint: first compute the probability of finding no defectives in the sample.
To determine the probability of finding at least one defective bulb in the lot of 100 bulbs, one must calculate the complementary event, picking no defective bulbs, and subtract its probability from 1.
Explanation:This problem involves Probability and Combinatorics, fundamental branches in Mathematics to calculate the possible outcomes in an event. Here, to calculate the probability of finding at least one defective bulb, we can begin by calculating the complementary event, that is, finding no defective bulbs in a sample.
The total number of ways to pick 10 bulbs from 100 is the combination C(100, 10). Likewise, the total number of ways to pick 10 non-defective bulbs from the 95 non-defective bulbs in the lot is C(95, 10). The probability of picking 10 non-defective bulbs then is C(95, 10)/C(100, 10).
Since the event of finding 'at least one defective bulb' is the complementary of 'finding no defective bulbs', we can subtract this probability from 1. So, the probability of finding at least one defective bulb is 1 - (C(95, 10)/C(100, 10)).
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A body oscillates with simple harmonic motion along the x-axis. its displacement varies with time according to the equation x(t) = a sin(ω t + φ). if a = 5 m, ω = 3.444 rad/s, and φ = 1.0472 rad, what is the acceleration of the body at t = 3 s? note: the argument of the sine function is in radians rather than degrees. answer in units of m/s 2 .
The acceleration of the body at t = 3 seconds is approximately [tex]\( -58.58785 \, \text{m/s}^2 \).[/tex]
To find the acceleration of the body at ( t = 3 ) seconds, we need to find the second derivative of the displacement function [tex]\( x(t) \)[/tex] with respect to time t.
Given that[tex]\( x(t) = a \sin(\omega t + \phi) \)[/tex] , where [tex]\( a = 5 \) m, \( \omega = 3.444 \) rad/s, and \( \phi = 1.0472 \)[/tex] rad, the acceleration a(t) is the second derivative of of x(t) with respect to t:
First, let's find the first derivative of of x(t) with respect to t:
[tex]\[ v(t) = \frac{dx}{dt} = a \omega \cos(\omega t + \phi) \][/tex]
Now, let's find the second derivative of x(t) with respect to t:
[tex]\[ a(t) = \frac{d^2x}{dt^2} = -a \omega^2 \sin(\omega t + \phi) \][/tex]
Now, substitute the given values:
[tex]\[ a(t) = -5 \times (3.444)^2 \sin(3.444 \times 3 + 1.0472) \][/tex]
Now, calculate:
[tex]\[ a(t) = -5 \times (3.444)^2 \sin(10.332 + 1.0472) \]\[ a(t) = -5 \times (3.444)^2 \sin(11.3792) \][/tex]
Now, compute:
[tex]\[ a(t) = -5 \times (11.858736) \sin(11.3792) \]\[ a(t) \approx -5 \times (11.858736) \times 0.97989 \]\[ a(t) \approx -58.58785 \, \text{m/s}^2 \][/tex]
Therefore, the acceleration of the body at t = 3 seconds is approximately [tex]\( -58.58785 \, \text{m/s}^2 \).[/tex]
If A2 = I, where I is the identity matrix, which matrix correctly represents matrix A?
We know that [tex] \boldsymbol{A^2}=\boldsymbol{A\times A} [/tex]
We also know that [tex] \boldsymbol{I}=\begin{bmatrix}
1 &0 \\
0&1
\end{bmatrix} [/tex]
Now, it has been given to us that [tex] \boldsymbol{A^2}=\boldsymbol{I} [/tex]
Therefore, we will have to find the correct [tex] \boldsymbol{A} [/tex] from the given options and we find that when:
[tex] \boldsymbol{A}=\begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix} [/tex]
then [tex] \boldsymbol{A^2}=\boldsymbol{A\times A}=\begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix}\times \begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix}=\begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix} [/tex]
Therefore, from the above given options, Option C is the correct option.
Therefore, [tex] \boldsymbol{A}=\begin{bmatrix}
3 & -2\\
4 & -3
\end{bmatrix} [/tex] is the correct answer.
Answer:
C. [3, -2]
[4, -3]
Step-by-step explanation:
PLATOOOO
A video sharing website starts with 20,000 members. Each year it loses 25% of the members, but adds 10,000 new members after the reduction. Write a recursive rule to find the number of members for any year.
Final answer:
To find the number of members for any year on the video sharing website, use the recursive rule with a base case of 20,000 initial members and apply the recursive step Mₙ = 0.75 × Mₙ₋₁ + 10,000 for each subsequent year.
Explanation:
The situation described can be modeled with a recursive rule where each year's membership is based on the previous year's membership.
To write such a rule, we'll use Mn to denote the number of members in year n, and Mn-1 to denote the number of members in the previous year.
The recursive rule is as follows:
Base case: M0 = 20,000 (initial number of members)Recursive step: Mₙ= 0.75 × Mₙ₋₁ + 10,000 for n > 0This means that for any year n, the number of members is equal to 75% of the previous year's members plus an additional 10,000 new members.
Helpp! Find the area. The figure is not drawn to scale. https://courses.jmhs.com/content/enforced/8012-MA042_20_1/group/45b8c516-1008-46d7-aa1d-bb9b62c786ff/geometry_exam_10_files/mc001-1.jpg?_&d2lSessionVal=vtelKg4rpW3IHn6Wnb7kcJRAw
A 56.24 cm2
B 3.9 cm2
C 11.3 cm2
D 28.12 cm2
You borrow $3200 to buy new kitchen appliances. The simple interest rate is 5%. You pay the loan off after 4 years.
The total amount paid = $3840
What is simple interest formula?"A = P(1 + rt)
Where A = Total Amount (principal + interest)
P = Principal Amount
I = Interest Amount
r = Rate of Interest in decimal
R = Rate of Interest as a percent
[tex]r=\frac{R}{100}[/tex]
t = Time Period"
For given question,
P = $3200
t = 4 years
R = 5%
[tex]\Rightarrow r=\frac{5}{100}\\\\ \Rightarrow r=0.05[/tex]
Using the formula of simple interest,
[tex]A=P(1+rt)\\\\A=3200(1+(0.05\times 4))\\\\A=3200(1+0.2)\\\\A=3200\times 1.2\\\\A=\$ 3840[/tex]
Therefore, the total amount paid = $3840
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a rectangular prism has a volume of 175 in3. The height of the prism is 7 in. The base is a square. What is the length of a side of the base?
after school, maurice walks 1/3 mile to the park and then walks 1/2 mile to his house. how far does maurice walk from school to his house?
The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi.
This is an incomplete question, here is the complete question.
The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi.
(1) 1727 cm²
(2) 2355 cm²
(3) 2041 cm²
(4) 6699 cm²
Answer : The surface area of the figure is, 1727 cm²
Step-by-step explanation :
The formula for curved surface area of triangle is:
[tex]A=\pi \times r\times l[/tex]
where,
r and l are radius and slant height of triangle.
The formula for curved surface area of cylinder is:
[tex]A=2\pi \times r\times h[/tex]
where,
r and h are radius and height of cylinder.
The formula for area of circle is:
[tex]A=\pi r^2[/tex]
where,
r is radius circle.
Now we have to calculate the surface area of total figure.
Surface area of total figure = Surface area of triangle + Surface area of cylinder + Area of circle
Surface area of total figure = [tex]\pi \times r\times l+2\pi \times r\times h+\pi r^2[/tex]
Surface area of total figure = [tex]\pi \times r(l+2h+r)[/tex]
Given:
r = 10 cm
h = 16 cm
l = 13 cm
Now put all the given values in this formula, we get:
Surface area of total figure = [tex]3.14\times 10\times (13+2\times 16+10)[/tex]
Surface area of total figure = 1727 cm²
Thus, the surface area of the figure is, 1727 cm²
A manufacturer of drinking glasses ships his delicate stock in speical boxes that can hold 32 glasses. if 1714 glasses are manufactured, how many full boxes are filled? are there any glasses left over?
The Chang's neighbor owns a ready-mix company. The company receives an order for 12.5 cubic yards of concrete. This mixture of concrete contains sand, cement, gravel, and water. For each pound of water, there are 5.5 pounds of sand, 2 pounds of cement, and 7.5 pounds of gravel. Determine how many pounds of cement must be used. Assume a cubic yard of concrete weighs 4,000 pounds.
A single gram of a certain substance has 0.52 gram of copper and 0.26 gram of zinc. The remaining portion of the substance.is nickel.Ben estimated that 0.2 gram of nickel is in 1 gram of the subtance.he used this estimate the amount of nickel in 35 grams of the substance.find the result of bens estimation strategy.then find the exact amoumt of nickel in 35 grams of the subtance
which will result in a diffrent of squares
Angle A=11x-4, Angle B = 4x-11, and Angle C=63-4x. List the sides of triangle ABC in order from shortest to longest.
A. AB, AC, BC
B. AC, AB, BC
C. BC, AB, AC
D. AB, BC, AC
A baseball team has three different pitchers. Randy pitched 333 innings and allowed 222 runs, Felix pitched 555 innings and allowed 444 runs, and Johan pitched 777 innings and allowed 555 runs.
Which pitcher has the lowest number of runs allowed per inning?
Answer: the andswer is randy
Step-by-step explanation:
Find the differential of the function. v = 2y cos(xy)
The differential of the function v = 2y cos(xy) is found using the product rule and the chain rule, yielding dv = 2 cos(xy) dy - 2y sin(xy) (xdy + ydx), which accounts for changes with respect to both x and y.
To find the differential of the function v = 2y cos(xy), we'll need to apply the product rule and the chain rule. The product rule states that the differential of a product of two functions is d(uv) = u dv + v du. The chain rule is used when differentiating composite functions, and it implies that d/dx (f(g(x))) = f'(g(x)) * g'(x).
Applying the product rule, we get:
dv = cos(xy) * d(2y) + 2y *d(cos(xy)).The differential d(2y) is simply 2 dy.For d(cos(xy)), we use the chain rule and get -sin(xy) * d(xy), which further expands to -sin(xy) * (xdy + ydx) by applying the product rule again.Combining these, the differential dv becomes:
dv = 2 cos(xy) dy - 2y sin(xy) (xdy + ydx).
This equation represents the total differential of the function v with respect to both x and y.
For implicit differentiation examples like in equation In(xy) = x2y3 or systems of differential equations, understanding and applying the product rule, chain rule, and implicit differentiation are essential to calculate derivatives and solve the equations.
The diagram is a hat box that is designed with the shape of a regular octagon inside and a rectangle outside. Find the value of x. Please explain.
Which function represents a vertical stretch of an exponential function? A. f(x)=3(1/2)^x B. f(x)=1/2(3)^x C. f(x)=(3)^2x D. f(x)=3^(1/2x)
Answer:
A. f(x) = 3*(1/2)^x
Step-by-step explanation:
We know that, a function can be stretched or shrinked both horizontally and vertically.
Now, according to our question we are required to look at the vertical stretch of an exponential function.
The general form for a vertical stretch of a function f(x) is k*f(x) where k>1.
So, we compare this form with the options provided.
We see that in option A the exponential function is multiplied by 3 and so the function will be stretched vertically.
Hence, option A is correct.