A sports recreation company plans to manufacture a beach ball with a surface area of 7238 in.2 find the radius of the beach ball. use the formula , where a is the surface area and r is the radius of the sphere. 576 in. 48 in. 75 in. 24 in.
The given problem supplies as with the surface area of the beach ball and we are to look for the required radius. Assuming that the beach ball is perfectly shaped in the form of a sphere, then the formula for calculating the surface area of a sphere is given as:
SA = 4 π r^2
where r is the radius of the sphere and SA is the surface area which is given to be 7238 in^2
Rewriting the formula in terms of r:
r^2 = SA / 4 π
r = sqrt (SA / 4 π)
Solving for r:
r = sqrt (7238 in^2 / 4 π)
r = 24 in
Answer:
24 inches
Which graph represents the solution to the system of inequalities? x + y ≥ 4 2x + 3y < 12
find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of negative 1
The point on the terminal side is (1,-1) and this can be determined by using the trigonometric functions.
Given :
The point on the terminal side of θ = negative three [tex]\pi[/tex] divided by four that has an x coordinate of negative 1.
The following steps can be used in order to determine the point on the terminal side:
Step 1 - Write the given expression.
[tex]\theta = -\dfrac{3\pi}{4}[/tex]
Step 2 - The value of the trigonometric function is given by:
[tex]\rm tan \dfrac{3\pi}{4} =-1[/tex]
Step 3 - The trigonometric function can also be written as:
[tex]\rm tan \theta=\dfrac{y}{x}=-1[/tex]
Step 4 - Substitute the value of 'x' in the above expression.
y = -1
So, the point on the terminal side is (1,-1).
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Figure ABCD is transformed to figure A′B′C′D′:
Which angle in Figure A′B′C′D′ is equal to Angle CDA.?
Angle D prime A prime B prime.
Angle A prime B prime C prime.
Angle B prime C prime D prime.
Angle C prime D prime A prime.
Answer:
I think it is Angle B prime C prime D prime
Step-by-step explanation:
A'B'C'D' is a translation so they are congruent.So the figure B'C'D' is congruent or equal to BCD. Please let me know if i'm right
You are 9 miles away from home. You start biking home at a speed of 6 miles per hour.
a. write an equation. in standard form that represents your distance from home y after x hours.
b. find the y-intercept of the graph. what does this represent?
c. find the x-intercept of the graph. what does this represent?
The distance and speed are illustrations of linear equations
The standard form is [tex]\mathbf{6x + y = 9}[/tex]The y-intercept is 9The x-intercept is 1.5The given parameters are:
[tex]\mathbf{Rate = 6}[/tex]
[tex]\mathbf{Initial = 9}[/tex]
(a) The standard equation
Because the distance reduces with time, the equation is:
[tex]\mathbf{y = Initial-Rate \times x}[/tex]
This gives
[tex]\mathbf{y = 9 - 6\times x}[/tex]
[tex]\mathbf{y = 9 - 6x}[/tex]
Add 6x to both sides
[tex]\mathbf{6x + y = 9}[/tex]
(b) The y-intercept
This is the initial distance away from home.
So, the y-intercept is 9
(c) The x-intercept
Set y to 0, to calculate the x-intercept
[tex]\mathbf{6x + y = 9}[/tex]
[tex]\mathbf{6x + 0 = 9}[/tex]
[tex]\mathbf{6x = 9}[/tex]
Divide both sides by 6
[tex]\mathbf{x = 1.5}[/tex]
This is the initial time away from home.
So, the x-intercept is 1.5
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An ice cream store sells 2 2 drinks, in 3 3 sizes, and 8 8 flavors. in how many ways can a customer order a drink?
If an ice cream store sells 2 drinks, in 3 sizes, and 8 flavors, the number of ways can a customer order a drink will be 48.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
It given that, An ice cream store sells 2 drinks, in 3 sizes, and 8 flavors.
We have to find the number of ways can a customer order a drink,
It is obtained by multiplying all the possible cases for that event, Multiplication is one type of arithmetic operation. There are basically four types of arithmetic operations.
=2×3×8
=48
Thus, if an ice cream store sells 2 drinks, in 3 sizes, and 8 flavors, the number of ways can a customer order a drink will be 48.
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A tree grows 1 3/4 feet per year. How long will it take the tree to grow from a height of 21 1/4 feet to a height of 37 feet?
Probability theory predicts that there is a 22.4% chance of a particular soccer player making four penalty shots in a row. If the soccer player taking four penalty shots is simulated 2500 times, in about how many of the simulations would you expect at least one missed shot?
1940 ~~~~~~~~~~~~ APEX
Find the slope in line perpendicular x-y=16
Use the table to determine the appropriate model of the function, x 1 2 3 4 5 f(x) 15 12 9 6 3 linear quadratic cubic exponential
The appropriate model of the function is:
Linear model
Step-by-step explanation:We are given a table of values as:
x f(x)
1 15
2 12
3 9
4 6
5 3
Clearly we could observe that with each increasing value of x the value of function decreases by 3.
This means that the range of change is constant.
Hence, the relation is linear ( as the rate of change is constant )
Also, the equation that models this data set is given by:
[tex]y=f(x)=18-3x[/tex]
Find the selling price of an item listed at $400 subject to a discounted series of $25%, 10%, and 5%
A. $256.50
B. $270.00
C. $225.00
D. $300.00
Answer:
Selling price of an item is $256.50 (A).
Step-by-step explanation:
Given : WE have given an item listed at $400 subject to a discounted series of $25%, 10%, and 5% .
To find : Find the selling price of an item.
Formula used : Selling price = marked price - discount.
Solution : We have an item listed at = $400.
Discount percentage = $25% , $10% , $5.
Discount 1 = $400 ×[tex]\frac{25}{100}[/tex] = $100.
Selling price = $400-100 = $300.
Discount 2 = $300 ×[tex]\frac{10}{100}[/tex] = $30.
Selling price = $300-30 = $270.
Discount 3 = $270 ×[tex]\frac{5}{100}[/tex] = $13.50.
Final selling price = $270-13.50 = $256.50.
Therefore, Selling price of an item is $256.50 (A).
Larry travels 60 miles per hour going to a friend’s house and 50 miles per hour coming back, using the same road. he drove a total of 5 hours. what is the distance from larry’s house to his friend’s house, rounded to the nearest mile?
Final answer:
To find the distance from Larry's house to his friend's house, we use the relationship between distance, speed, and time for his trip to and from his friend's house, taking into account the different speeds and total travel time of 5 hours.
Explanation:
The student's question asks to find the distance from Larry's house to his friend's house given his speed and total travel time in both directions. To solve this problem, we use the formula distance = speed × time. Let's call the distance one way d, the time to travel to the friend's house t1, and the time to travel back t2. Larry's speed going to the friend's house is 60 miles per hour and coming back is 50 miles per hour. The total travel time is 5 hours.
So for the trip to the friend's house we have:
d = 60 × t1
And for the trip back:
d = 50 × t2
Since the total travel time is 5 hours:
t1 + t2 = 5
Substituting the expressions for d from the first two equations into the third, we get:
60t1 + 50t2 = 60(5)
Using the fact that t1 + t2 = 5, we solve for either variable, say t1, which gives us t2 as well. After finding t1 and t2, we plug either of those back into the original distance equations to find d, which will be the distance from Larry's house to his friend's house. The answer should be rounded to the nearest mile.
Use basic identities to simplify the expression. sin^2θ + tan^2θ + cos^2θ
slope of -8 and Y intercept of (0, 12) in slope intercept form.
The length of a rectangle is 22 meters longer than the width. if the area is 2626 square meters, find the rectangle's dimensions. round to the nearest tenth of a meter.
Can someone simplify 2y-3x^2+6x^2-3y ?
help me plox 20 points
if they were rounded to the tens place
18 would round to 20
16 would round to 20
17 would round to 20
14 would round to 10
so April would be different.
please help me idk how to do this at all I've been stuck on it for awhile.
when numbers are in parenthesis the first number is x the second is y
(x,y)
sine they give you (2, blank)
2 = x so replace x in the equation with 2
so y=2x+5 becomes y=2(2)+5
so y = 2*2+5 = 9
y=9
so it should be (2,9)
Find an exact value. sin(17pi/12)
a. √6 - √2 / 4
b. -√6 - √2 / 4
c. √6 + √2 / 4
d. √2 - √6 / 4
The required exact value of the given trigonometric function is sin(17π/12) = (√6 + √2)/4
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The trigonometric function is given in the question, as follows:
sin(17π/12)
To find the value of sin(17π/12), we can use the following trigonometric identity:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
In this case, we can write:
sin(17π/12) = sin(π/3 + π/4)
We know that sin(π/3) = √3/2 and cos(π/3) = 1/2, and sin(π/4) = cos(π/4) = √2/2.
Therefore, we can use the above identity to get:
sin(17π/12) = sin(π/3)cos(π/4) + cos(π/3)sin(π/4)
= (√3/2)(√2/2) + (1/2)(√2/2)
= (√6/4) + (√2/4)
= (√6 + √2)/4
So the answer is option (c): √6 + √2 / 4.
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A ball is thrown from a height of 140 feet with an initial downward velocity of 8 ft/s. The ball's height h (in feet) after t seconds is given by the following.
h=140-8t-16t^2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
The time would be 2.71 seconds after the ball is thrown does it hit the ground.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
A ball is thrown from a height of 140 feet with an initial downward velocity of 8 ft/s.
The ball's height h (in feet) after t seconds is given by the following.
⇒ h = 140-8t - 16t²
h = 0 at the ground.
We divide both sides of the equation by (-8) to yield:
⇒ 0 = 2t² + t - 17.5
where a = 2, b= 1, c = -17
[tex]t = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\t = \dfrac{-1\pm\sqrt{2^2-4\times2\times-17.5}}{2\times2}[/tex]
t = [-1 ± √141] / (4)
t = 2.71 and -3.21
For this problem, time can only be positive, so ignore the negative solution.
Therefore, the time would be 2.71 seconds after the ball is thrown does it hit the ground.
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Probability theory predicts that there is a 44% chance of a water polo team winning any particular match. If the water polo team playing 2 matches is simulated 10,000 times, in about how many of the simulations would you expect them to win exactly one match?
Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 13 in. by 8 in.
You and six friends play a game where each person writes down his or her name on a scrap of paper, and the names are randomly distributed back to each person. Find the probability that everyone gets back his or her own name.
Answer with explanation:
Total number of different candidates who are playing the game=7
Suppose, Seven candidates are represented by ={A,B,C,D,E,F,G}
Total Possible Outcome =7
→Probability that , "A" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{7}[/tex]
→Now, 6 candidates are left.
Probability that , "B" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{6}[/tex]
→Now, 5, candidates are left.
Probability that , "C" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{5}[/tex]
→Now, 4 candidates are left.
Probability that , "D" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{4}[/tex]
→Now, 3 candidates are left.
Probability that , "E" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{3}[/tex]
→Now, 2 candidates are left.
Probability that , "F" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{2}[/tex]
→Now, a single candidates is left.
Probability that , "G" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{1}=1[/tex]
Required Probability
[tex]=\frac{1}{7} \times\frac{1}{6} \times\frac{1}{5} \times\frac{1}{4} \times\frac{1}{3} \times\frac{1}{2} \times 1\\\\=\frac{1}{5040}[/tex]
Kenji buys 3 yards of fabric for 7.47$. Then he realizes that he needs 2 more yards. How much will the extra fabric cost?
True or false an inscribed angle is formed by two radii that share an endpoint
True or false an inscribed angle is formed by two radii that share an endpoint
the correct answer is : FALSE
Answer:
The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.
Step-by-step explanation:
Inscribed angle is a angle which is formed inside the circle by joining of two intersecting chords inside a circle.
The inscribed angle is explained with the help of a diagram below :
In the diagram attached below, ∠ABC is an inscribed angle with an intercepted minor arc from A to C.
Thus, the inscribed angle is not formed with the help of radii that share a common end point.
Hence, The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.
Hey there! I would like some help please :) Thanks!
Given the functions f(x) = 3x2, g(x) = x2 − 4x + 5, and h(x) = –2x2 + 4x + 1, rank them from least to greatest based on their axis of symmetry. f(x), g(x), h(x) f(x), h(x), g(x) g(x), h(x), f(x) g(x), f(x), h(x)
Answer:
f(x), h(x), g(x)
Jessica attains a height of 4.7 feet above the launch and landing ramps after 1 second. Her initial velocity is 25 feet per second. Find the angle of her launch. a. Which equation can you use with the given information to solve for ?
A 31-in. television has a 31 in. diagonal and a 18 in. width. what is the height of the 31-in. television?
Write a segment addition problem using three points that asks the student to solve for x but has a solution x = 20
The segment addition problem was given below which gives the value of x as 20.
Segment addition problem:
Consider three points on a line: A, B, and C. Point B is located between points A and C.
The lengths of the line segments are as follows:
Length of segment AB: 12
Length of segment BC: x
Length of segment AC: 32
Find the value of x.
We have the equation for segment addition: AB + BC = AC
Substitute the given values:
12 + x = 32
Now, solve for x:
x = 32 - 12
x = 20
Therefore, the value of x is indeed 20, and the lengths of the segments satisfy the segment addition property.
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To construct a segment addition problem with a solution of x = 20, use three collinear points A, B, and C and set AB = x and BC = 20 - x, with the entire segment AC being 20 units. Solving the equation x + (20 - x) = 20 confirms that x = 20 is the solution.
Explanation:To write a segment addition problem that solves for x where the solution is x = 20, let’s use three collinear points A, B, and C with point B between A and C. We can then express the lengths of segments AB and BC in terms of x. For instance, if AB is x units long and BC is 20 - x units long, the total length of AC would be 20 units. We can write an equation based on this:
AB + BC = AC
x + (20 - x) = 20
By simplifying, x cancels out on the left-hand side, leaving 20 = 20, which is true for x = 20. Therefore, this is a valid segment addition problem where solving for x yields 20 as the solution.
Here is the step-by-step problem phrased as a question:
Let points A, B, and C be collinear with B between A and C.If AB = x and BC = 20 - x, and AC = 20, find the value of x.