Answers
[tex]\boxed{A}\\\\ U=5(2n+22)+2\left( n+\cfrac{3}{2} \right) \\\\\\ U=10n+110+2n+3 \implies U=12n+113 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\hspace{5em}\textit{in 2009, that's 9 years after 2000, n = 9}\\\\ U(9)=12(9)+113\implies U(9)=221 ~~ millions[/tex]
Related Questions
The darkness of the print is measured quantitatively using an index. If the index is greater than or
equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and
not acceptable. Assume that the machines print at an average darkness of 2.2 with a standard
deviation of 0.20.
(a) What percentage of printing jobs will be acceptable? (4)
(b) If the mean cannot be adjusted, but the standard deviation can, what must be the new standard
deviation such that a minimum of 95% of jobs will be acceptable?
Answers
84.13% of the printing jobs will be acceptable.
The new standard deviation required to achieve a minimum of 95% of jobs acceptable is 0.121.
The darkness of the print is measured quantitatively using an index. If the index is greater than or equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and not acceptable. The machines print at an average darkness of 2.2 with a standard deviation of 0.20.
The mean of the darkness of the print is µ = 2.2 and the standard deviation is σ = 0.20.Therefore, the z-score can be calculated as; `z = (x - µ) / σ`.The index required for acceptable prints is 2.0. Thus, the percentage of prints that are acceptable can be calculated as follows;P(X ≥ 2.0) = P((X - µ)/σ ≥ (2.0 - 2.2) / 0.20)P(Z ≥ -1) = 1 - P(Z < -1)Using the standard normal table, P(Z < -1) = 0.1587P(Z ≥ -1) = 1 - 0.1587= 0.8413.
To find the new standard deviation, we can use the z-score formula.z = (x - µ) / σz = (2.0 - 2.2) / σz = -1Therefore, P(X ≥ 2.0) = 0.95P(Z ≥ -1) = 0.95P(Z < -1) = 0.05Using the standard normal table, the z-score value of -1.645 corresponds to a cumulative probability of 0.05. Hence,z = (2.0 - 2.2) / σ = -1.645σ = (2.0 - 2.2) / -1.645= 0.121.
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what is the y intercept of y=7
Answers
Answer:
7
Step-by-step explanation:
The line represented by the equation y = 7 is a horizontal line that passes through the y-axis at 7, so the y intercept of this line is 7
Nina and Ryan each ran at a constant speed for a 100-meter race. Each runner’s distance for the same section of the race is displayed on the left. Who had a head start, and how big was the head start?
had a head start of
meters.
Answers
Answer:
Ryan had a head start of 10 meters
Step-by-step explanation:
Twice the difference of a number 9 and 2 is . Use the variable b for the unknown number.
Answers
answer: 13/2 or 6 1/2
step-by-step explanation:
hihi so basically your problem is making a solvable equation so w variables and stuff
heres my explanation !
the difference of a number and 2 is b-2
twice the difference of a number and 2 would be 2(b-2)
number 9 = 9 (duh lol)
so
2(b-2) = 9
2b - 4 = 9
2b = 13
improper: b = 13/2
mixed: b = 6 1/2
Which graph represents the function?
f(x)=x√+1
Answers
The graph of the function f(x)=√(x + 1) is in the first option
What is a radical graphA radical graph, also known as a square root graph, represents the graph of a square root function. A square root function is a mathematical function that takes the square root of the input variable.
The general form of a square root function is f(x) = √(ax + b) + c,
where a, b, and c are constants that determine the characteristics of the graph.
In the given function:
a = 1
b = 1
c = 0
The graph is plotted and attached
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URGENT
The area of a kite is 180 cm^2. The length of one diagonal is 16cm. What is the length of the other diagonal?
SHOW WORK AND ANSWER PLEASE
Answers
The length of the other diagonal is 11.25 cm.
What is area?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
In this question, we are given the following:
The area of a kite is 180. One of the diagonals is 16.
What is the length of the other diagonal?
The details of the solution are as follows:
We know that,
The area of a kite is the product of the diagonals divided by 2:
[tex]\text{A} = \dfrac{(\text{d}^1 \times \text{d}^2)}{2}[/tex]
You can substitute what we have:
[tex]180= \dfrac{(16 \times \text{d}^2)}{2}[/tex]
And solve.
[tex]180 = 16 \times \text{d}^2[/tex]
[tex]\text{d}^2=\dfrac{180}{16}[/tex]
[tex]\text{d}^2=\bold{11.25 \ cm}[/tex]
Therefore, the length of the other diagonal = 11.25 cm.
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Write the English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The product of 8 and a number, which is then subtracted from the product of 17 and the number.
Answers
The algebraic expression for the given phrase is: 17x - 8x. To simplify this expression, we can combine like terms by subtracting the coefficients of x. The simplified expression is: 9x.
In the given phrase, "The product of 8 and a number" can be represented as 8x, where x represents the number. Similarly, "The product of 17 and the number" can be represented as 17x. Since we are subtracting the product of 8x from the product of 17x, the algebraic expression becomes 17x - 8x.
To simplify the expression, we combine like terms. The coefficients of x are 17 and -8. Since we are subtracting 8x from 17x, we subtract the coefficient of 8x from the coefficient of 17x, resulting in 17x - 8x. Combining like terms gives us 9x.
In conclusion, the simplified expression for the phrase "The product of 8 and a number, which is then subtracted from the product of 17 and the number" is 9x.
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Patricia serves the volleyabll to terri with an upward velocity of 19.5 ft/s . The ball is 4.5 feet above the ground when she strikes it. How long does terri have to react before the volleyball hits the ground ? Round your answer to gwo decimal places
Answers
Terri have to react 1.42 seconds before the volleyball hits the ground.
What are quadratic equations?Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is:
[tex]\text{ax}^2 + \text{bx} + \text{c} = 0[/tex]
Given data:
Velocity [tex](v_0)[/tex] = 19.5 ft/sHeight [tex](h_0)[/tex] = 4.5 ftThe height can be modeled by a quadratic equation.
[tex]h(t)=-16t^2+v_0t+h_0[/tex]
Where h is the height and t is the time.
[tex]h(t)=-16t^2+19.5t+4.5[/tex]
[tex]-16t^2+19.5t+4.5=0[/tex]
[tex]a = -16, b = 19.5, c = 4.5[/tex]
It looks like a quadratic equation. we can solve it by quadratic formula.
[tex]\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\rightarrow t=\dfrac{-19.5\pm\sqrt{(-19.5)^2-4\times(-16)(4.5)} }{2(-16)}[/tex]
[tex]\rightarrow t=\dfrac{-19.5\pm\sqrt{380.25+288} }{-32}[/tex]
[tex]\rightarrow t=\dfrac{-19.5\pm25.851 }{-32}[/tex]
[tex]\rightarrow t=\dfrac{-19.5-25.851 }{-32}, \ t=\dfrac{-19.5+25.851 }{-32}[/tex]
[tex]\rightarrow t=1.42, \ t=-0.20[/tex]
Time cannot be in negative. So neglect t = –0.235.
Hence, Terri have to react 1.42 seconds before the volleyball hits the ground.
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Using the physics concept of projectile motion and inputting the given values into the appropriate equation, we can determine the time it takes for the volleyball to hit the ground after being served
Explanation:This question is a classic use of physics, more specifically, the concept of projectile motion. Here, the volleyball can be conceived as a projectile. When Patricia serves the ball upward, the ball will first ascend and then descend due to gravity.
Let's use the following equation which is a version of kinematic equations to solve this problem, adjusting for the fact that we're dealing with an initial height of 4.5 ft and an ending height of 0 ft (when the ball hits the ground). The equation y = yo + vot - 0.5gt² , where:
y is the final vertical position (which we'll take to be 0),yo is the initial vertical position (in this case, the 4.5 feet above the ground),vo is the initial vertical velocity, t is the time (which we're trying to find), andg is the acceleration due to gravity, with the value approximately 32.2 feet per second squared.
Setting y=0, yo=4.5 feet, vo=19.5 feet/second, and g=32.2 feet/second², and plug these values into the equation, we'll get a quadratic equation in the form of 0 = 4.5 + 19.5t - 16.1t². Solve that equation for t to find the time it takes for the ball to hit the ground.
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To find the number in a square, add the numbers in the two circles
connected to it.
Fill in the missing numbers.
Answers
The missing values in the quantitative reasoning given are : -2, 13 and 9
Given the rule :
square = circle + circleWe can deduce that :
circle = square - circleFor the left circle :
circle = -6 - (-4) = -6 + 4 = -2
For the right circle :
circle = 11 - (-2) = 11 + 2 = 13
For the left square :
square = 13 + (-4)
square = 13 -4 = 9
Therefore, the missing values are : -2, 13 and 9
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