David’s score at the end of round 3 is calculated by adding the net points gained during the round to his initial score, resulting in a final score of 2000 points.
Calculating David's Score
To determine David's score at the end of round 3, we need to account for both his correct answers and incorrect answers during the round.
David's initial score at the start of round 3 is -1500 points.
During round 3:
He answered five 1000-point questions correctly. Each correct answer adds 1000 points. So, 5 correct answers add:
5 × 1000 = 5000 points
He answered three 500-point questions incorrectly. Each incorrect answer subtracts 500 points. So, 3 incorrect answers subtract:
3 × 500 = 1500 points
Next, we calculate the net change in his score by adding the points gained and subtracting the points lost:
Net change = 5000 points (gained) - 1500 points (lost) = 3500 points
Finally, we add this net change to his initial score:
Final score = -1500 points (initial score) + 3500 points (net change) = 2000 points
Thus, David's score at the end of round 3 is 2000 points.
Express terms in i square root -40
It takes 69 pounds of seed to completely plant an 8 -acre field. how many acres can be planted per pound of seed? math
Use your calculator to evaluate the limit of x equals 1 to 3 of e raised to the x squared power, dx. Give your answer to the nearest integer.
Numerical Answers Expected!
What is the greatest common factor of 125, 50, and 275?
Answer:
25 is the greatest common factor.
Step-by-step explanation:
We are given the following information in the question:
We have t find the greatest common factor of 125, 50 and 275.
We can use the method of prime factorization.
[tex]125 = 5\times 5\times 5\\50 = 5\times 5\times 2\\275 = 5\times 5\times 11[/tex]
Hence, the common factor of the the three numbers are:
[tex]5\times 5 = 25[/tex]
Hence, the greatest common factor 125, 50, 275 is 25.
Directions: Use a proportion to solve the problem.
Emily weighs six times as much on Earth as she does on the Moon. If her weight is ninety pounds on earth, what would her weight be on the moon?
Select "Growth" or "Decay" to classify each function.
Function Growth Decay
y=200(0.5)^2t
y=1/2(2.5)^t/6
y=(0.65)^t/4
Which equation can be used to find the solution of (1/3)^d−5 = 81 ?
A. −d−5=4
B. d + 5 = 4
C. d−5=4
D. −d+5=4
1. The growth rate equation has a general form of:
y = A (r)^t
The function is growth when r≥1, and it is a decay when r<1. Therefore:
y=200(0.5)^2t --> Decay
y=1/2(2.5)^t/6 --> Growth
y=(0.65)^t/4 --> Decay
2. We rewrite the given equation (1/3)^d−5 = 81
Take the log of both sides:
(d – 5) log(1/3) = log 81
d – 5 = log 81 / log(1/3)
d – 5 = - 4
Multiply both sides by negative 1:
- d + 5 = 4
So the answer is D
During a certain period of time, a car can cover the distance of 120 miles, going at an average speed of 55 mph. What distance over the same period of time would cover a truck, going at an average speed of 44 mph?
HELP WITH SOLVING SYSTEMS WITH THREE VARIABLES, WILL MEDAL
-x -y -z = -8
-4x + 4y + 5z = 7
2x + 2z = 4
I'm not sure how to work this out.
Which of the following expressions represents the value, in dollars, of a certain number of dimes, d, and pennies, p?
0.01d + 0.10p
0.10d + 0.01p
0.11dp
0.11d + p
What is the expression phrase of the sum of a number x and 4, all divided by 3?
Which ordered pairs are solutions to the inequality y−4x≥−5 ?
Select each correct answer.
(5, −2)
(1, −1)
(−4, 2)
(4, 0)
(−2, 1)
The ordered pairs that satisfy the given inequality is required.
The points that are solutions are [tex](-4,2),(-2,1),(1,-1)[/tex]
The given inequality is [tex]y-4x\geq -5[/tex]
Let us substitute each point in the inequality
[tex](5,-2)[/tex]
[tex]y-4x\\ =-2-4\times 5\\ =-22\ngeq -5[/tex]
[tex](1,-1)[/tex]
[tex]-1-4\times 1\\ =-5\geq -5[/tex]
[tex](-4,2)[/tex]
[tex]2-4\times -4\\ =18\geq -5[/tex]
[tex](4,0)[/tex]
[tex]0-4\times 4=-16\ngeq -5[/tex]
[tex](-2,1)[/tex]
[tex]1-4\times -2=7\geq -5[/tex]
The points that are solutions are [tex](-4,2),(-2,1),(1,-1)[/tex]
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Estimate the unit rate
What is a 401(k) plan? an investment plan offered by an insurance company a retirement plan offered by employers a personal retirement plan
A) choose the linear model that passes through the most data points on the scatterplot.
a. true. choose the linear model that passes through the most data points on the scatterplot.
b. false. the line usually touches none of the points. minimize the sum of the squared errors.
c. false. all of the data points either touch the line or fall below the line.
d. false. the linear model line usually passes through exactly half of the data points.
Final answer:
The correct statement relating to the selection of a linear model is that the line of best fit is found using the least-squares method to minimize the sum of squared errors. This involves plotting data points, calculating the least-squares regression line, and determining if the linear model fits the data appropriately.
Explanation:
The question pertains to the selection of a linear model based on a provided scatterplot. The correct choice is b. false. the line usually touches none of the points. minimize the sum of the squared errors. This statement refers to the concept of least-squares regression, a mathematical method used to find the line of best fit by minimizing the squared differences (errors) between the observed values and the values predicted by the model. This line is intended to predict the dependent variable based on the independent variable. The process includes plotting the data, calculating the least-squares line, and determining if the linear model is appropriate for the data set.
After plotting the data points on a scatter plot, we use a calculator or statistical software to compute the least-squares regression line, represented as ŷ = a + bx, where a is the y-intercept, b is the slope, and ŷ is the predicted value of the dependent variable for any given value of the independent variable. The line may not pass through the most data points, but instead represents the trend of the data points in a way that minimizes the overall error of the model.
The line passing through the points (-7,4) and (-23,y) is parallel to a line that has a slope of -5/8. What is the value of y?
Simplify the expression x^2+3x-28/x^2-7x+12
Answer:
[tex]\frac{x+7}{x-3}[/tex].
Step-by-step explanation:
We have been given an expression. We are asked to simplify our given expression.
[tex]\frac{x^2+3x-28}{x^2-7x+12}[/tex]
Let us factor numerator and denominator by splitting the middle term.
[tex]\frac{x^2+7x-4x-28}{x^2-4x-3x+12}[/tex]
[tex]\frac{(x^2+7x)+(-4x-28)}{(x^2-4x)+(-3x+12)}[/tex]
Factor out GCF of each group:
[tex]\frac{x(x+7)-4(x+7)}{x(x-4)-3(x-4)}[/tex]
[tex]\frac{(x+7)(x-4)}{(x-4)(x-3)}[/tex]
Cancel out common factor [tex](x-4)[/tex]:
[tex]\frac{(x+7)}{(x-3)}[/tex]
Therefore, the simplified form of the given expression would be [tex]\frac{x+7}{x-3}[/tex].
Point F is on circle C.
What is the length of line segment GF?
a.12.5 units
b.15.0 units
c.17.5 units
d.20.0 units
Answer:
GF = 20 units .
Step-by-step explanation:
Given : A circle ,Point F is on circle C.
To find : What is the length of line segment GF.
Solution : We have given A circle ,Point F is on circle C.
In circle we can see in triangle GCE
EC = CF = 7.5
GE = 10.
By the Pythagorean theorem :
GC² = EG²+ EC².
Plugging the values
GC² = 10²+ 7.5².
GC² = 100 + 56 .25.
GC² = 156.25.
Taking square root.
GC = 12.5 units.
Radius of circle CF = 7.5 units .
GF = GC +CF.
GF = 12.5 + 7.5
GF = 20 units .
Therefore, GF = 20 units .
Helpp me with this word problem number one
factor completely: x^3+8x^2+7x
Which of the following phrases could represent the expression k - 4?
A.a number subtracted from four
B.four less a number
C.a number decreased by four
D.a number less than four
the diagram below shows a rectangle inside a regular hexagon . the apothem of the hexagon is 19.05 units . to the nearest square unit . what is the area of the shaded region
A. 1257
B.861
C.442
D.1653
Answer:
B. 861.Step-by-step explanation:
In the figure attached, you can observe that the shaded area can be found by calculating the difference between the area of the regular hexagon and the area of the rectangle inside.
The area of a regular hexagon is defined as
[tex]A_{hexagon} =\frac{Pa}{2}[/tex]
Where [tex]P[/tex] is the perimeter and [tex]a[/tex] is the apothem.
By given, we know that the side of the hexagon is 22 units.
Remember that the perimeter is the sum of all sides, in this case would be
[tex]P_{hexagon}=22(6) =132[/tex].
The perimeter of the hexagon is 132 units.
Therefore, the area is
[tex]A_{hexagon} =\frac{132(19.05)}{2}=\frac{2514.6}{2}=1257.3 u^{2}[/tex]
On the other hand, the area of the rectangle is defined as
[tex]A_{rectangle}=bh[/tex], where [tex]b[/tex] is the base and [tex]h[/tex] is the height. We know, by given
[tex]b=22\\h=18[/tex]
Replacing these values, we have
[tex]A_{rectangle}=bh=22(18)=396 u^{2}[/tex]
As we said before, the shaded are is defined by the following difference
[tex]A_{shaded}=A_{hexagon}-A_{rectangle}[/tex]
Replacing each area, we have
[tex]A_{shaded}=A_{hexagon}-A_{rectangle}\\A_{shaded}=1257.3u^{2} -396u^{2}=861.3 u^{2}[/tex]
Therefore, the right answer is B. 861.
Child development
What have researchers learned about the relationship between longer childhoods and brain development?
Longer childhoods are closely linked to brain development, enhancing cognitive abilities by allowing more complex neuronal connections and greater adaptation to environmental stimuli. Extended brain development is also associated with increased brain plasticity, leading to better adaptability and higher complex problem-solving skills.
Explanation:Research has found a significant relationship between longer childhoods and brain development. Humans have one of the longest childhoods among species, a period during which our brains continue to develop and mature significantly. This extended period of growth allows for more complex neuronal connections and adaptation to environmental stimuli, thus enhancing cognitive abilities.
A long childhood provides ample opportunities for learning and skill acquisition, and it is during this period that the brain is especially receptive to picking up new information. More prolonged brain development during childhood also tends to be associated with increased brain plasticity, meaning the brain's ability to change and adapt as a result of experiences. This plasticity aids in the formation of our identities and equips us to handle complex tasks and challenges as we grow.
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How to find the values of the six trigonometric functions for 180?
Trisha needs 4 yards of fabric to do a project. If she already has of a yard of fabric, what is the minimum amount of fabric she must buy to be able to complete her project? A. 3 5/6 B.4 1/12 C.4 1/6
Answer:
The answer is A. OR 3 5/6
One third of the sum of two consecutive odd integers is five less than the smaller integer
As Marta built a square fence around her garden, she wondered how much she would have to pay if she increased the length of each side of the fence by the same number of meters. Each meter of fence costs 3 dollars. Which of the following functions best describes the additional amount of money Marta will have to spend, in dollars, if she increases each side of the fence by m meters?
When writing the slope as a fraction which numner goes on top?
The number goes on top tells line changes in the y direction and how much it rises.
what is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
As, The top number indicates how much the line rises or moves in the y direction.
Given that the number is a 1 and is positive, we can infer that the line rises or moves up by one.
Hence, line changes in the y direction and how much it rises.
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Which improper fraction is equal to the mixed number 4 7/9 btw its a mixed number fraction
A. 37/9
B. 47/9
C. 43/9
D. 20/9
plz help asap
HELP! A daycare purchases two type of snacks, granola bars and fruit rolls. One week, they purchase 10 packs of granola bars and 6 packs of fruit rolls for a total of 152 snacks. The next week, they purchase 7 packs of granola bars and 12 packs of fruit rolls for a total of 200 snacks. How many snacks are in one pack of granola bars and one pack of fruit rolls?
Answer: The number of granola bars in one pack = 8
The number of fruit rolls in one pack = 12
Step-by-step explanation:
Let x be the number of granola bars in each pack and y be the number of fruit rolls in each pack .
Then according to the question we have the following system of equations :
[tex]10x+6y=152.....................(1)\\7x+12y=200.......................(2)[/tex]
Multiply equation (1) by 2 we get
[tex]20x+12y=304......................(3)[/tex]
Subtract equation (2) from equation (3), we get
[tex]13x=104\\\\\Rigtarrow x=8[/tex]
Substitute x=8 in (1), we get
[tex]10(8)+6y=152\\\\\Rightarrow6y=152-80\\\\\Rightarrow\ 6y=72\\\Rightarrow y=12[/tex]
Hence, the number of granola bars in one pack = 8
The number of fruit rolls in one pack = 12
Hadlee got 18 out of 20 questions correct on her math quiz. What percent of the questions did she get right?