The problem involves setting up an equation based on the given situation to solve for the number of baseball cards Neil and Larry have. By solving the equation, you find that Larry has 400 cards and Neil has 320 cards. So, they have 720 baseball cards together.
Explanation:This is a problem of percentages and of algebra. First, you know that the number of cards Neil has is 80% of what Larry has. This can be set up as an algebraic equation, where N represents Neil’s cards and L represents Larry’s cards: N = 0.8L. You also know that Neil has 80 fewer cards than Larry, which provides a second equation: N = L - 80.
Because both expressions equal N, you can set them equal to each other to solve for L. This leads to 0.8L = L - 80. Solve this equation for L, and you get L = 400. Substituting this into the equation N = 0.8L, you find that N = 320. Therefore, Neil and Larry have 720 baseball cards altogether.
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The slope of the line passing through the points (6, -1) and (7, -2) is
Which table represents the second piece of the function f(x)
Answer:
Third table represents the second piece of the function f(x)
Step-by-step explanation:
The second piece of the function f(x) is [tex]f(x)=8-2x[/tex]
Now, we substitute some values of x and find the corresponding function values and check which table satisfy the points.
For x = 1
[tex]f(1)=8-2(1)\\f(1)=6[/tex]
For x = 2
[tex]f(2)=8-2(2)\\f(2)=4[/tex]
For x = 3
[tex]f(3)=8-2(3)\\f(3)=6[/tex]
Among the given tables, third tables contains these values.
Third table represents the second piece of the function f(x)
Solve for x: 8x + 10 - 5x = 15.
8x+10-5x = 15
3x+10 = 15
3x = 5
x = 5/3
Julio is playing a trivia game .on his first turn ,he lost 100 points on his second turn ,he lost 75 points . On his third, he lost 85 points. Write a sum of three nagative integer that models the change to julio score after his first three turns
Find an equation of the vertical line that passes through (x, y) = (5, 11).
Find the diameter of a cone that has a volume of 83.74 cubic inches and a height of 5 inches. use 3.14 for pi. (1 point) 3 inches 4 inches 8 inches 16 inches
Answer: 8 inches
Step-by-step explanation:
The volume of a cone is given by :-
[tex]\text{Volume}=\dfrac{1}{3}\pi r^2 h[/tex], where r is radius and h is height of the cone.
Given : The volume of cone = 83.74 cubic inches
The height of cone = 5 inches
Then by using the above formula , we have
[tex]83.74=\dfrac{1}{3}(3.14) r^2 5\\\\\Rightarrow\ r^2=\dfrac{3\times83.74}{3.14\times5}\\\\\Rightarrow\ r^2=16.0012738854\approx16\\\\\Righatrrow\ r=\sqrt{16}=4\text{ inches}[/tex]
Diameter of cone = [tex]2r=2(4)=8\text{ inches}[/tex]
Hence, the diameter of cone = 8 inches
what are the discontinuities of the function f(x) =x<2-36/4x-24 ?
If you apply the changes below to the absolute value parent function, F(x)=|x|, what is the equation of the new function? Shift 8 units left, shift 3 units down.
A. G(x)=|x-3|-8
B. G(x)=|x-3|+8
C. G(x)=|x-8|-3
G(x)=|x+8|-3
Question 1(Multiple Choice Worth 5 points) (07.05 HC)
The work of a student to solve the equation 3(2x − 4) = 8 + 2x + 6 is shown below: Step 1: 3(2x − 4) = 8 + 2x + 6 Step 2: 5x − 7 = 14 + 2x Step 3: 5x − 2x = 14 + 7 Step 4: 3x = 21 Step 5: x = 7 In which step did the student first make an error and what is the correct step?
Step 2; 6x − 12 = 14 + 2x
Step 2; 6x − 7 = 2(6 + x + 4)
Step 3; 5x − 2x = 14 − 7
Step 3; 5x + 2x = 14 + 7
Geometry please help !!
A boat makes a 120-mile trip downstream in 3 hours but makes the return trip in 4 hours. If b = the rate of the boat in still water and c = the rate of the current, which of the following equations represents the trip downstream?
3(b - c) = 120
3(b + c) = 120
4(b + c) = 120
Is 70 thousand written in standard form or word form explain.
In circle Y, what is m?
59°
67°
71°
118°
Answer:
[tex]arc\ TU=71\°[/tex]
Step-by-step explanation:
we know that
The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite
In this problem we have that
[tex]63\° =\frac{1}{2}(arc\ SR+arc\ TU)[/tex]
we have
[tex]arc\ SR=55\°[/tex]
substitute and solve for arc TU
[tex]63\° =\frac{1}{2}(55\°+arc\ TU)[/tex]
[tex]126\° =(55\°+arc\ TU)[/tex]
[tex]arc\ TU=126\°-55\°=71\°[/tex]
a rectangle has a perimeter of 182 in and length of 52 in. What is the width?
A reflecting telescope is purchased by a library for a new astronomy program. The telescope has a horizontal parabolic frame and contains two mirrors, 3 inches apart from each other- the first in the base and the second at the focal point. The astronomy teacher would like to attach a digital monitoring system on the edge of the telescope, creating a straight line distance above the focal point. Assuming that the telescope is placed on the edge of the roof in such a way that it is parallel to the ground, the position of the monitoring system, in relationship to the distance between the base and the focal point is modeled by the equation, x = 1/12y2 (x = the distance between the base and the focal point; y= the height of the monitoring system).
Rewrite the model so that the height of the digital monitoring system is a function of the distance between the base and the focal point of the telescope. How high above the focal point is the digital monitoring system attached to the telescope? Include your function and the height, rounded to the nearest tenth of an inch, in your final answer.
The digital monitoring system attached at 6 inch from telescope.
What is Parabola?A curve produced by the intersection of a cone's surface with a plane perpendicular to a straight line; a curve produced by a moving point whose distance from a stationary point is equal to its distance from a fixed line.
Here, we have a parabolic frame with the focus point and on the tip from the stem coming from its center, the digital monitoring system.
So, the equation that in this situation is
x = y² / 12
12x = y²
y= √12x
So, at x= 3 the y will be
y = √12(3)
y = √36
y = 6
Thus, the digital monitoring system attached at 6 inch from telescope.
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A ball is dropped from the top of a 550 ft. building. The function h(t) = - 16t2 + 50 models the height of the ball, h(t) (in feet), at any given time, t (in seconds).
What is the maximum height of the ball?
550 ft
423 ft
Find the value of x. Express your answer in simplest radical form
A bacteria culture starts with 120 and after 3 hours the population consists of 200 bacteria. What is the rate of the increase to the nearest percent?
The rate of the increase would be 18.56% to the nearest percent.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Seema obtained a score of 57% on her exam, that corresponds to 67 out of 100.
We have been given 120 bacteria to start, which increases to 200 bacteria in 3 hours.
The population-increasing formula is given by
⇒ P(n) = P₀(1+ r)ⁿ
Here P(n) = 200, P₀ = 120, and n = 3
Substitute the values in the above equation,
⇒ 200 = 120(1+ r)³
⇒ 200 / 120 = (1+ r)³
⇒ 5/3 = (1+ r)³
⇒ ∛5/3 = 1+ r
⇒ ∛5/3 - 1 = r
⇒ r = 0.18563
⇒ % r = 18.56%
Therefore, the rate of the increase would be 18.56% to the nearest percent.
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The rate of increase for a bacteria culture that starts with 120 bacteria and grows to 200 after 3 hours is calculated by dividing the increase in population (80) by the initial population (120) and then multiplying by 100 to get the percentage. The rate of increase is 66.67%, which rounds to 67% to the nearest percent.
To find the rate of increase to the nearest percent for a bacteria culture that starts with 120 bacteria and grows to 200 bacteria after 3 hours, we must calculate the percentage growth over the time period given.
First, we need to find the absolute increase in the number of bacteria:
Final population - Initial population = Increase in population
200 - 120 = 80
Next, we calculate the rate of increase based on the initial population:
(Increase in population / Initial population)
(80 / 120)
Multiplying by 100 to get the percentage: (80 / 120) ×100
Rate of increase = 66.67%
Rounded to the nearest percent, the rate of increase is 67%
Each marble bag sold by leila's marble company contains 5 yellow marbles for every 8 green marbles. if a bag has 35 yellow marbles, how many green marbles does it contain?
What are the difference between polynomial long division and arithmetic long division?
Answer:
The purpose of long division with polynomials is similar to long division with integers; to find whether the divisor is a factor of the dividend and, if not, the remainder after the divisor is factored into the dividend. The primary difference here is that you are now dividing with variables.
write a function g whose graph represents a translation 2 units to the right followed by a horizontal stretch by a factor or 2 on the graph of f(x)=|x|
The graph of the function g(x) = 2(|x - 2|) represents a translation 2 units to the right followed by a horizontal stretch by a factor of 2 on the graph of f(x) = |x|.
Explanation:To represent a translation 2 units to the right followed by a horizontal stretch by a factor of 2 on the graph of f(x) = |x|, we can define the function g(x) as g(x) = 2(|x - 2|).
The function |x - 2| represents the translation 2 units to the right, while the factor of 2 in front of the absolute value represents the horizontal stretch by a factor of 2.
For example, when x = 1, g(x) = 2(|1 - 2|) = 2(|-1|) = 2.
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There is a traffic light at the intersection of Walnut Street and Lawrence Avenue. The traffic light on Walnut Street follows a cycle. It is green for 50 seconds, yellow for 10 seconds, and red for 30 seconds. As you travel along Walnut and approach the intersection, what is the probability that the first color you see is red?
1/5
1/3
3/5
1/2
After John worked at a job for 10 years, his salary doubled. If he started at $ x , his salary after 10 years is _____.
$ x
$ x + 2
$ x - 2
$2 x
The sum of the page numbers on the facing pages of a book is 81. what are the page? numbers?
Solve the following system by any method. 8x + 9y = –5 –8x – 9y = 5 A. (–10, 3) B. (–3, 10) C. (0,0) D. Infinitely many solutions
Your class has 30 students. if 1313 of them walk to school, how many students in your class walk to school?
Answer:10
Step-by-step explanation:
Given the points A (3,2) and B (-21,0) determine:
a. the slope of line AB
b. the length of AB
c. the midpoint of AB
d. an equation of AB
Which should come next at the end of this row of letters: a b d g?
Answer:
Next letter will be k.
Step-by-step explanation:
we have to find the letter which will come next at the end of the row of letters
a b d g.
First we will write the alphabets as below to understand the sequence
a b c d e f g h i j k
Between a and b alphabet skipped = 0
Between b and d alphabets skipped = 1 (c)
Between d and g skipped alphabets = 2 (e and f)
Therefore after g number of alphabets skipped will be = 3 (h i j)
Next alphabet will be k.
The height of 18-year-old men are approximately normally distributed, with mean of 68 inches and a standard deviation of 3 inches. what is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? round your answer to the nearest thousandths place (3 places).the height of 18-year-old men are approximately normally distributed, with mean of 68 inches and a standard deviation of 3 inches. what is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? round your answer to the nearest thousandths place (3 places).
The probability of an 18-year-old man selected at random being between 67 and 69 inches tall is approximately 0.261.
Here's how we can calculate this:
Standardize the values: Convert the heights of 67 inches and 69 inches to z-scores using the formula:
z = (x - mean) / standard deviation.
In this case, z for 67 inches is -0.33 and z for 69 inches is 0.33.
Calculate the area between the z-scores: Using a standard normal distribution table or calculator, find the area between -0.33 and 0.33. This represents the probability of an 18-year-old man having a height within that range.
Round the answer: The calculated area is approximately 0.261, which is the probability of a randomly selected man being between 67 and 69 inches tall.
Therefore, the probability of an 18-year-old man selected at random being between 67 and 69 inches tall is approximately 0.261.
The probability that an 18-year-old man selected at random is between 67 and 69 inches tall is approximately 0.259.
To find the probability that an 18-year-old man selected at random is between 67 and 69 inches tall, we first need to standardize the values using the z-score formula:
[tex]\( z = \frac{x - \mu}{\sigma} \)[/tex]
where x is the value
[tex]\( \mu \)[/tex] is the mean, and
[tex]\( \sigma \)[/tex] is the standard deviation.
For x = 67 inches: [tex]\( z = \frac{67 - 68}{3} = -0.333 \)[/tex]
For x = 69 inches: [tex]\( z = \frac{69 - 68}{3} = 0.333 \)[/tex]
Using the standard normal distribution table or calculator, we find the corresponding probabilities:
P(z < -0.333) and P(z < 0.333)
P(z < -0.333) = 0.3707 and P(z < 0.333) = 0.6293
To find the probability between 67 and 69 inches, we subtract the smaller probability from the larger:
0.6293 - 0.3707 = 0.2586
The dot plot shows the number of words students spelled correctly on a pre-test. Which statement best describes the shape of the graph?
A.) The graph is skewed right.
B.) The graph is nearly symmetrical.
C.) The graph is skewed left.
D.) The graph is perfectly symmetrical.
Let's think of this problem easily by looking at it instead of going through rigorous mathematics.
When a graph is skewed right, most of the values are to the left side.
When a graph is skewed left, most of the values are to the right side.
Perfectly symmetrical is that both sides, with respect to the median, are same. Here mean and median is equal.
Nearly symmetrical would really close to perfect symmetry, only varying a bit on both sides. Mean would be approximately equal to median.
Now counting the dots as well as looking closely, we can rule out skewed right and skewed left. Now, is the graph perfectly symmetrical? No! So the correct answer is "nearly symmetrical". Correct choice is B.
ANSWER: B
Answer:
The answer is neary symmetrical or answer B
Step-by-step explanation:
If you cut the graph in half exactly, both side would almost line up perfectly.