Suppose you went to a carnival. The price to get in was $6, and you paid $0.50 to get on each ride. If you went to the carnival and rode 11 rides, how much did you spend?
The total money that would be spent for 11 rides in the carnival be $11.5
As mentioned in the question, the price to get in was $6, and you paid $0.50 to get on each ride.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the total money paid for 11 rides,
= 0.5 × 11 = $5.5
Total money spent on the carnival,
= 6 + 5.5 = $11.5
Thus, the total money that would be spent for 11 rides in the carnival be $11.5.
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A traffic light near a museum is green for 30 seconds, yellow for 5 seconds, and red for 15 seconds.
If 8 vehicles approach the signal, the probability that 3 of them are stopped by the red light is
If 8 vehicles approach the signal, the probability that 3 of them are stopped by the red light is:
0.25412184
Step-by-step explanation:Here we need to use the binomial theorem.
i.e. the probability of k successes out of total n experiments is calculated by the formula:
[tex]P(X=k)=n_C_kp^k(1-p)^{n-k}[/tex]
where p is the probability of successes.
Here we have p=Probability that signal is red.
i.e. p=15/50=3/10=0.3
Hence, 1-p=0.7
Also we have: n=8
and k=3
Hence,
[tex]P(X=3)=8_C_3\times (0.3)^3(0.7)^{8-3}\\\\\\P(X=3)=\dfrac{8!}{3!\times (8-3)!}\times (0.3)^3\times (0.7)^5\\\\\\P(X=3)=\dfrac{8!}{3!\times 5!}\times 0.00453789\\\\\\P(X=3)=0.25412184[/tex]
Hence, the probability is:
0.25412184
Ms. Purdy bought coffee and orange juice for her coworkers in her office.She bought X cups of coffee at $2 per cup and Y cups of orange juice at $1.50 per cup. Altogether she spent $30. Interpret the X- and the Y- Intercepts
Final answer:
The X-intercept of the equation 2X + 1.5Y = 30 represents the maximum number of cups of coffee that can be bought with $30 if no orange juice is purchased (15 cups), and the Y-intercept represents the maximum number of orange juice cups that can be bought with $30 if no coffee is purchased (20 cups).
Explanation:
When Ms. Purdy purchased coffee and orange juice for her coworkers, she created a budget constraint based on the respective prices and her total spending. With X representing the number of cups of coffee purchased at $2 each and Y representing the cups of orange juice purchased at $1.50 each, the equation for her total expenditure is 2X + 1.5Y = 30.
The X-intercept occurs when no orange juice is purchased (Y=0), and the total budget is spent on coffee.
This can be calculated by setting Y to 0 in the equation, resulting in X = 15.
The Y-intercept occurs when no coffee is purchased (X=0), which can be found by setting X to 0, leading to Y = 20.
Thus, the X-intercept represents the maximum number of cups of coffee that can be purchased with the $30 budget if no orange juice is bought, while the Y-intercept shows the maximum number of cups of orange juice that could be purchased with the same budget if no coffee is bought.
Choose the correct simplification of (4x − 3)(3x2 − 4x − 3).
12x3 + 25x2 + 9
12x3 − 25x2 − 9
12x3 + 25x2 − 9
12x3 − 25x2 + 9 Choose the correct simplification of (4x − 3)(3x2 − 4x − 3).
12x3 + 25x2 + 9
12x3 − 25x2 − 9
12x3 + 25x2 − 9
12x3 − 25x2 + 9
Answer: [tex]12x^3-25x^2+9[/tex]
Step-by-step explanation:
Given expression: [tex](4x-3)(3x^2-4x-3)[/tex]
To simplify the above expression we apply the distributive property [ (b+c)a=ba+ca, where a,b, c be any expression] we get ,
[tex](4x-3)(3x^2-4x-3)\\\\=4x(3x^2-4x-3)-3(3x^2-4x-3)\\\\=12x^{1+2}-16x^{1+1}-12x-9x^2+12x+9.......\text{[by law of exponents]}\\\\=12x^{3}-16x^{2}-12x-9x^2+12x+9\\\\\text{Combing like terms, we get}\\\\=12x^3-(16+9)x^2-12x+12x+9\\\\=12x^3-25x^2+9[/tex]
Answer:
[tex]12x^{3}-25x^{2}+9[/tex]
Step-by-step explanation:
1. Write down the equation:
[tex](4x-3)(3x^{2}-4x-3)[/tex]
2. Multiply the first term on the left parenthesis by each term on the right parenthesis:
[tex]4x*3x^{2}=12x^{3}[/tex]
[tex]4x*(-4x)=-16x^{2}[/tex]
[tex]4x*(-3)=-12x[/tex]
3. Multiply the second term on the left parenthesis by each term on the right parenthesis:
[tex]-3*(3x^{2})=-9x^{2}[/tex]
[tex]-3*(-4x)=12x[/tex]
[tex]-3*(-3)=9[/tex]
4. Add up all the terms:
[tex]12x^{3}-16x^{2}-12x-9x^{2}+12x+9[/tex]
Simplify:
[tex]12x^{3}-25x^{2}+9[/tex]
Bruce reads 3fourths hour each night.how long will he read in 4 nights
Find the area of the striped sector if ∠ A = 45° and the circle has a radius of 10 inches.
A)25π
B)5π over 4
C)5π over 2
D)25π over 2 ...?
Answer: D) 25π
Step-by-step explanation:
Got this right on USA test prep
How to solve inequaities?
Given the function, f(x)=[square root] x+3-2 , calculate the average rate of change between x=6 and x=13.
Answer:
Average rate for the given function is 1 / 7
Step-by-step explanation:
The average exchange rate corresponds to the ratio between the variation of the function and the variation of the variable. That is to say,
Average rate = [f (x2) - f (x1)] / (x2 -x1). Since x1 = 6 and x2 = 13, you have:
f (x1) = f (6) = sqrt (6 + 3) - 2 = 3 - 2 = 1
f (x2) = f (13) = sqrt (13 + 3) - 2 = 4 - 2 = 2
In this way,
Average rate = (2 -1) / (13 - 6) = 1/7
Does a plane have a definite beginning and end?
In mathematics, a plane is a two-dimensional surface with no definite beginning or end, extending infinitely in all directions. The properties of a plane, such as the loss of the usual 1/² dependence, are abstract and not physically tangible. Examples of motion, like an airplane passenger's movement or the effect of wind on a plane's trajectory, can help visualize concepts related to planes.
Explanation:When considering the concept of a plane in mathematics, it is important to understand its properties. A plane is a flat, two-dimensional surface that extends infinitely in all directions. It does not have a definite beginning or end, meaning there is no bounded border that marks where it starts or stops. This idea can be difficult to conceptualize because it is abstract and not something we encounter in the physical world. In terms of geometry, we often approach problems involving planes by considering a portion of the plane that is relevant to the problem. For example, the concept of an infinite plane becomes intriguing as it affects the mathematical properties, such as the loss of the usual 1/² dependence encountered in finite plane calculations. To illustrate motion in a plane, one might analyze the average velocity of an object, such as an airplane passenger moving from the front to the back of an airplane or the influence of wind on a plane's trajectory relative to the ground. These scenarios involve physical planes and motions, but they help to visualize the movements within the mathematical context of planes.
What is the answer for -0.04 times -0.1?
Which number families does the number 1 belong to??
expand 4(x+3)+6(x+2)
Copycats copies charges $.18 for the first copy and $.12 for each additional copy what is the greatest number of copies you can get for three dollars
Calculate cos to two decimal places
A ball bearing is shaped like a sphere and has a diameter os 2.5 centimeters l. What is the volume contained inside the ball bearing? Use 3.14 pi. Round your answer to the nearest hundredth
The volume of the ball bearing, which is a sphere, would be approximately 8.18 cm³. This is calculated using the formula for the volume of a sphere and the given diameter, which is halved to get the radius for the calculation
Explanation:The volume of a sphere can be calculated using the formula V = 4/3 * π * r³, where r is the radius of the sphere. In this case, the diameter of the ball bearing is 2.5 cm, so the radius would be half of that (diameter/2), which is 1.25 cm. Substituting the radius value to the volume formula, we get: V = 4/3 * π * (1.25cm)³ = 4/3 * 3.14 * 1.95cm³ = approximately 8.18 cm³, rounded to the nearest hundredth.
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A sprinter can run 279 feet in 9 seconds. Find the sprinter's unit rate of feet per second.
To find the sprinter's unit rate of feet per second, divide the total distance by the time. In this case, the sprinter's unit rate is approximately 31 feet per second.
Explanation:To find the sprinter's unit rate of feet per second, we need to divide the total distance the sprinter can run by the time it takes. In this case, the sprinter can run 279 feet in 9 seconds. So the unit rate is 279 feet divided by 9 seconds, which is approximately 31 feet per second.
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simplify 7j-6k-5j+4k which explanation please:)
For exercises 19-24, y varies directly with x
if y = 25 when x = 15, find y when x = 6.
Help me explain how to do it step by step !
Donald earns a commission of 3.7% on all sales above his weekly quota of $12,500. his sales last week totaled $32,480. what commission amount did Donald earn last week?
Donald earned a commission of $739.26 last week.
Explanation:To calculate the commission amount earned by Donald last week, we need to find the sales above his weekly quota first. Sales above the quota is calculated by subtracting the weekly quota from the total sales. In this case, $32,480 - $12,500 = $19,980. Next, we can calculate the commission amount by multiplying the sales above the quota by the commission rate. The commission amount earned by Donald last week is $19,980 * 0.037 = $739.26.
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The distance from the library to the park is 0.7 kilometers how much meters is this
How do you make 1 3/4 an improper fraction?
Ben wants to buy 2 blue sweaters for 119$ and 3 brown sweaters for 44$ each how much will ben spend on his five sweaters?
A Jeweler has 36 inches of silver chain. She needs 5 times much to make some necklaces and 3 times that amount to make some bracelets. How much does the jeweler need to make her necklaces and bracelets
Step-by-step explanation:
Five years ago, William bought a twelve-room apartment complex for $340,000, and he plans to sell it today. The real estate market caused William’s complex to increase in value by 1.8% every year. William charges $525 per month to rent a room, and pays $36,500 in building upkeep every year. If William has kept all of his apartments continually rented out since he bought the building, to the nearest hundred dollars, how much profit will he realize once he sells it?
a.
$195,500
b.
$227,200
c.
$226,100
d.
$245,500
Answer:
THE ANSWER IS B ON EGDE
Step-by-step explanation:
Answer:
Edging b
Step-by-step explanation:
. Evaluate 9C5
126
24
3024
120
...?
Answer:
126 is the answer please give me brainliest.
Step-by-step explanation:
Related Rates
A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 2.1 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
once you have that relation, then you can replace the variables by the numbers given. by similar triangles that relation is
y12=2x then differentiate both sidesA circle has a central angle measuring 3pi/4 radians that intersects an arc of length 45 in. What is the length of the radius of the circle?
Math question: Write the equation of the line with an undefined slope, passing through the point (2, 5).
The equation of a line with an undefined slope passing through the point (2, 5) can be written as x = 2.
When the slope of a line is undefined, it means that the line is vertical. In a vertical line, the x-coordinate remains constant while the y-coordinate can take any value.
So, for this line passing through the point (2, 5), the x-coordinate will always be 2, regardless of the value of y. Therefore, we can represent this line with the equation x = 2.
The sum of two numbers is 27. the larger number is 6 more than twice the smaller number. what are the numbers?
TRUE or FALSE.
Based only on the information given in the diagram, it is guaranteed that ΔABC ≈ ΔXYZ.
It is a true statement that it is guaranteed that ΔABC ≈ ΔXYZ in the diagram given.
Why will ΔABC equals ΔXYZ?In this context, all triangles have 180 degrees altogether in as much they have a standard size of the shape.
The triangles have the sames standard size although the letters of the angles are different.
Therefore, the statement is a true statement.
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Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not exist, enter DNE.)
f (x) = x2 + 9x − 4 relative minimum
(x, y) =
relative maximum (x, y) =
please help me
...?
Final answer:
To find the relative minimum of the function, we first calculate its first derivative and set it to zero to find critical points. A single critical point is found at x = -9/2. Using the Second Derivative Test, we conclude that there is a relative minimum at (-9/2, -97/4) since the function's second derivative is positive, indicating the function is concave up at this point.
Explanation:
To find the relative extrema of the function f(x) = x2 + 9x − 4, we first need to determine its critical points. This is done by finding the derivative of f(x) and setting it equal to zero.
The derivative of the function, f'(x), can be calculated as follows:
f'(x) = 2x + 9
Setting the derivative equal to zero gives us:
2x + 9 = 0
x = -9/2
Now, we apply the Second Derivative Test to determine if this critical point is a relative maximum or minimum. The second derivative is:
f''(x) = 2
Since the second derivative is positive, the function is concave up at x = -9/2. Therefore, the function has a relative minimum at this point.
To find the y-coordinate, we substitute x = -9/2 into the original function:
f(-9/2) = (-9/2)2 + 9*(-9/2) − 4
Simplifying this, we get:
y = 81/4 - 81/2 - 4
y = 81/4 - 162/4 - 16/4
y = -97/4
Therefore, the relative minimum is (-9/2, -97/4). There is no relative maximum since the function is a parabola that opens upwards.