1. Write the equation in standard form:
\(\begin{gathered} \text{Add 156 in both sides of the equation:} \\ -4x^2-40x+156=-156+156 \\ \\ -4x^2-40x+156=0 \end{gathered}\)2. Identify the coefficients a, b and c:
\(\begin{gathered} ax^2+bx+c=0 \\ \\ \text{For the given equation:} \\ a=-4 \\ b=-40 \\ c=156 \end{gathered}\)3. Substitute the values into the quadratic equation:
\(x=\frac{-(-40)\pm\sqrt[]{(-40)^2-4(-4)(156)}}{2(-4)}\)4. Solve the equation for x1 and x2:
\(\begin{gathered} x_{}=\frac{-(-40)\pm\sqrt[]{(-40)^2-4(-4)(156)}}{2(-4)} \\ \\ x_{}=\frac{40\pm\sqrt[]{1600+2496}}{-8} \\ \\ x=\frac{40\pm\sqrt[]{4096}}{-8} \\ \\ x=\frac{40\pm64}{-8} \\ \\ \\ x_1=\frac{40-64}{-8}=\frac{-24}{-8}=3 \\ \\ x_2=\frac{40+64}{-8}=\frac{104}{-8}=-13 \end{gathered}\)Exact form and approximate form are the same for both solutions (x1 and x2):
\(\begin{gathered} x_1=3 \\ \\ x_2=-13 \end{gathered}\)One of the team members convinced you to use Logistic Regression instead of Classification Tree. What argument did the team member use to change your mind
The argument used by the team member was that a single line is used to differentiate the space into two. This is will make the presentation more attractive. Even if there are higher-dimensional data the lines will generalize into planes and hyperplanes. So according to the team member, it would be better to use Logistic Regression.
When we use the classification tree presentation the data will be mixed up and will clash against each other. So using the Logistic Regression will be better as this divides the data set into two separate parts. So, if the data are not linearly separable then only we should use the Classification Method.
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this article presents the results through sixth grade of a longitudinal randomized control study of the effects of a scaled-up, state-supported pre-k program. the analytic sample includes 2,990 children from low-income families who applied to oversubscribed pre-k program sites across the state and were randomly assigned to offers of admission or a wait list control. data through sixth grade from state education records showed that the children randomly assigned to attend pre-k had lower state achievement test scores in third through sixth grades than control children, with the strongest negative effects in sixth grade. a negative effect was also found for disciplinary infractions, attendance, and receipt of special education services, with null effects on retention
The given data of an article presents the findings of a longitudinal randomized control study on the impact of a scaled-up, state-supported pre-k program on low-income children.
The article reports the results of a longitudinal randomized control study investigating the effects of a state-supported pre-k program on low-income children. The study involved nearly 3,000 children who were randomly assigned to either attend pre-k or be placed on a waitlist control.
Analysis of data from state education records up to sixth grade revealed that children who attended pre-k had lower state achievement test scores in grades three to six compared to the control group. The negative effects were most prominent in sixth grade. Additionally, the study found that attending pre-k was associated with increased disciplinary infractions, poorer attendance, and higher rates of receiving special education services. However, there were no significant effects observed on grade retention.
In conclusion, the study highlights the concerning findings regarding the impact of the scaled-up pre-k program on low-income children. The lower achievement test scores and negative effects on disciplinary infractions, attendance, and special education services suggest that further examination and potential modifications to the program may be needed to improve outcomes for participating students.
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Which of the following is the concept illustrated with the misentered data? A. The procedure for constructing the confidence interval is not robust. The smaller the sample size, the less resistant the mean. Therefore, the confidence interval is more robust.
Answer:
B. Te procedure for constructing the confidence interval is robust. The larger the sample size, the more resistance the mean. Therefore, the confidence interval is more robust.
Step-by-step explanation:
Misentered data illustrates the concept that if the sample size is larger it will be more resistance to mean. This means confidence interval is more robust. In statistics, robust is a modification of confidence interval. It refers to strength of statistical model. Robust statistics is resistant to errors in statistical model.
HELP PLZ I’m struggling with this
Answer:
270 per year so 6 years is 1620 and add that with 6000=7620
A passenger plane made a trip to Las Vegas and back. On the trip there it flew 432 mph and on the return trip it went 480 mph. How long did the trip there take if the return trip took nine hours?
Answer:
10 hours
Step-by-step explanation:
Because if u divide the speed t= 4320miles/432mph=10h
Determine if the following triangle is acute, right, or obtuse.
Answer: It is an acute angle
Step-by-step explanation:
The angles are 45.35, 39.52, 95.13
A farmer goes to the market to sell a box of eggs. A clumsy horse steps on the box of eggs and breaks a lot of them. The horse’s rider offers to pay for all of the eggs in the box and asks the farmer how many eggs there were. The farmer does not remember the exact number, but when she took them out of the box two at a time, there was 1 egg left. The same thing happened when she took them out three, four, five and six eggs at a time, but when she took them out 7 at a time, there were no eggs left
The smallest number of eggs that could have been in the box is 1134
The problem is to find the smallest number of eggs that could have been in the box, given the remainder when taking them out by different numbers. Here are the moves toward tackling it:
Allow n to be the quantity of eggs in the container. Then we have the accompanying arrangement of congruences:
n ≡ 1 (mod 2)
n ≡ 1 (mod 3)
n ≡ 1 (mod 4)
n ≡ 1 (mod 5)
n ≡ 1 (mod 6)
n ≡ 0 (mod 7)
For this problem, we have k = 6 k = 6, a i = {1,1,1,1,1,0} a_i = {1,1,1,1,1,0}, M i = {1260,840,630,504,420,720} M_i = {1260,840,630,504,420,720}, and y i = {−1,−2,−3,-4,-5,-6} y_i = {-1,-2,-3,-4,-5,-6}.
Plugging these values into the formula and simplifying modulo 5040, we get:
n = (−1260 + −1680 + −1890 + −2016 + −2100 + 0) mod 5040
n = (−8946) mod 5040
n = (−3906) mod 5040
n = 1134 mod 5040
Therefore, the smallest number of eggs that could have been in the box is 1134
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Plot 5 points and show period
The x-values π/2, π, 3π/2, and 2π on the x-axis.
We have the function,
y = -6 sin (6/5)x + 6
The period of the sine function is 2π. This means one complete cycle occurs from 0 to 2π.
The amplitude of the function is 6, which represents the distance from the centerline (y = 6) to the maximum and minimum points.
Maximum value: y = 6 + 6 = 12
Minimum value: y = 6 - 6 = 0
The x-intercepts occur when y = 0.
Solve the equation -6sin(x) + 6 = 0 for x.
-6sin(x) = -6
sin(x) = 1
So, The x-values for which sin(x) = 1 are π/2 and 3π/2.
Then, an appropriate scale for the x-axis, such as intervals of π/2 or π/4.
Mark the x-values π/2, π, 3π/2, and 2π on the x-axis.
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Calculate the area and perimeter of each of the following polyons.
The area and perimeter of each of the given polygons are a) 12+2√3+√34 units, 32 units² and b) 27 units and 46 units²
What are polygons?A polygon is a two-dimensional geometric figure that has a finite number of sides.
Given that, two polygons, we need to calculate the area and perimeter of each of the following polygons.
1) Calculating the lengths of the side by using Pythagoras theorem,
Sides = 2√3, √34, 5, 5 and 2
Therefore, perimeter = 12+2√3+√34 units
Area =
The polygon is divided into a trapezium and a triangle,
Therefore,
Area = 1/2(8x3)+4/2(8+2) = 12+20 = 32 units²
2) Perimeter = 1+1+2+2+2+3+3+4+4+5 = 27 units
Area = (2x1)+(3x1)+(3x5)+(3x2)+(5x4) = 2+3+15+6+20 = 46 units²
Hence, the area and perimeter of each of the given polygons are a) 12+2√3+√34 units, 32 units² and b) 27 units and 46 units²
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-3+n ≥ -4n-3 or 3n-4≥4n + 1
Answer:
-3+n ≥ -4n-3
Step-by-step explanation:
its good to use a number for n
if n = 5
-3+n ≥ -4n-3 or 3n-4≥4n + 1
for
-3+n ≥ -4n-3
-3+5 ≥ -4(5)-3
-2 ≥ -20-3
-2 ≥ -23
true
for
3n-4≥4n + 1
3(5)-4≥4(5) + 1
15-4≥20 + 1
11 ≥20 + 1
11 ≥21
not true
all three vertices of an equilateral lie on the parabola defined by , with at the origin and parallel to the -axis. what is the area of the triangle?
we can substitute the side length into the formula for the area of an equilateral triangle to calculate the area.
To find the area of the equilateral triangle, we first need to determine the coordinates of its vertices.
Let's consider the vertex A of the equilateral triangle. Since it lies on the parabola defined by y = x^2, and it is parallel to the y-axis, its coordinates can be expressed as (x, x^2).
Since the triangle is equilateral, we can determine the coordinates of the other two vertices by rotating point A by 60 degrees clockwise and counterclockwise.
For the counterclockwise rotation, the coordinates of the second vertex B can be obtained by rotating point A by 60 degrees counterclockwise around the origin. Using the rotation formula, the coordinates of B will be:
B(x', y') = (xcos(60°) - x^2sin(60°), xsin(60°) + x^2cos(60°))
Similarly, for the clockwise rotation, the coordinates of the third vertex C can be obtained by rotating point A by 60 degrees clockwise around the origin. Using the rotation formula, the coordinates of C will be:
C(x'', y'') = (xcos(-60°) - x^2sin(-60°), xsin(-60°) + x^2cos(-60°))
Now, we have the coordinates of all three vertices of the equilateral triangle: A(x, x^2), B(x', y'), and C(x'', y''). To find the area of the triangle, we can use the formula for the area of an equilateral triangle:
Area = (sqrt(3) * side^2) / 4
In this case, the side length of the equilateral triangle can be determined by finding the distance between any two vertices.
Using the distance formula, the side length is given by:
side = sqrt((x' - x)^2 + (y' - x^2)^2)
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Which of the following is an arithmetic sequence with common difference 2?
O A. 1. -3,5, -7,9, ...
B. 2, 4, 8, 16, 32, ...
O C. 10, 8, 6, 4, 2, ...
D. 13, 15, 17, 19, 21, ...
HELP NEEDED!!!
Using the following table, what is the term that best describes the entry of 0.31?
Do you prefer dancing or playing sports?
Students | Playing sports | Dancing | Row totals
Male students | 0.25 | 0.27 | 0.52
Female students | 0.17 | 0.31 | 0.48
Column totals | 0.42 | 0.58 | 1
A.Joint frequency
B.Joint relative frequency
C.Marginal frequency
D.Marginal relative frequency
Evaluate the expression 4 x (9 ÷ 3) + 6 − 2 using PEMDAS. (1 point)
27
24
16
11
what is the decimal expansion for 16/30
If the area of a rectangle equals 30 cm² and the perimeter is equal to 26 cm. Find the length and width of the rectangle.
Answer:
Length = 10 & width = 3
Step-by-step explanation:
Perimeter = Length + Length + Width + Width
26 = 2Length + 2 Width
26 = 2 ( Length + Width )
13 = Length + width
13 - Length = Width EQUATION 1
Area = Length X Width
30 = Length X ( 13 - Length )
30 = 13Length - Length ^2
Length ^2 - 13Length + 30 = 0
( Length - 3 )( Length - 10 )
Length = 3 or Length = 10
Therefore Length = 10
From equation 1
13 - Length = Width
13 - 10 = width
width = 3
Which inequality is represented by the graph?
Which point is a solution to the inequality?
Answer:
there is no picture attached here I really wish I could help
Please help me this is urgent I will give all my points!
Answer:
See below
Step-by-step explanation:
Area of rectangle - area of semicircle =
25 x17 - 1/2 pi (3.5)^2 = 405.8 mm^2 to the nearest tenth ...
6+ax=-29 a=0 solve for x
The given equation solved for x is x = -25/a
Solving an EquationFrom the question, we are to solve for x in the given equation, provided that a≠0
The given equation is
6 + ax = -29
Solving the equation
6 + ax = -29
Subtract 6 from both sides
6 - 6 + ax = -29 - 6
ax = -25
Divide both sides of the equation by a '
ax/a = -25/a
x = -25/a
Hence, the solution is x = -25/a
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Your grandmother has been putting $5,000 into a savings account on every birthday since your first that is, when you turned one). The account pays an interest rate of 7% How much money will be in the account medialty after your grandmother makes the deposit on your 18th birthday The amount in the account upon your 18th birthday is (Round to the nearest dollar)
After your grandmother makes a $5,000 deposit on your 18th birthday, the amount in the savings account can be calculated using compound interest. Assuming the account pays an interest rate of 7%, the amount in the account immediately after the deposit can be determined by applying the compound interest formula.
To calculate the amount in the savings account after the deposit on your 18th birthday, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A represents the final amount, P is the principal (initial deposit), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, the initial deposit is $5,000, the interest rate is 7% (or 0.07 as a decimal), and the deposit is made on your 18th birthday, which means the time is 17 years. Since no information is given about the compounding frequency, let's assume it is compounded annually (n = 1).
Plugging in the values into the compound interest formula, we have A = 5000(1 + 0.07/1)^(1*17) = 5000(1.07)^17 ≈ $15,128.
Therefore, the amount in the savings account immediately after your grandmother makes the deposit on your 18th birthday is approximately $15,128, rounded to the nearest dollar.
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The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable. A mapping diagram with one circle labeled x-values containing values negative 4, negative 2, 0, 1, and 3 and another circle labeled y values containing values negative 5, negative 4, negative 3, negative 2, and negative 1 and arrows from negative 4 to negative 5, negative 2 to negative 3, 0 to negative 4, 0 to negative 2, 1 to negative 3, and 3 to negative 1. Is the relation a function? Explain. No, because for each input there is not exactly one output No, because for each output there is not exactly one input Yes, because for each input there is exactly one output Yes, because for each output there is exactly one input
As a result of answering the given question, we may state that No, equation because there isn't exactly one output for each input.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides separated by an equals sign (=). For example, the equation "2x + 3 = 9" argues that the expression "2x + 3" is equal to the value "9". The purpose of equation solving is to determine the value or values of the variable(s) that make the equation true. Simple or complex equations, linear or nonlinear, and involving one or more variables are all possible. For example, the quadratic equation "x2 + 2x - 3 = 0" involves the variable x raised to the second power. Equations are utilised in many areas of mathematics, such as algebra, calculus, and geometry.
To test whether the relationship is a function, we must examine whether each input (x-value) has precisely one output (y-value).
The mapping diagram shows that input -4 is related with output -5, but input 0 is associated with two separate outputs, -4 and -2. Similarly, the input 1 is linked to -3, but the input -2 is likewise linked to -3. As a result, the relation is not a function because some inputs have several outputs.
As a result, the right answer is:
No, because there isn't exactly one output for each input.
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what is the quadratic pattern difference?
Answer:
+4
Step-by-step explanation:
The equation for the points is \(y=2x^{2}+1\) and the quadratic pattern difference is +4. Attached is an image with the work to get to this answer.
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a 13-foot ladder is leaning against a wall. if we pull the ladder away from the wall at a rate of 6ft/s, how fast is the top of the ladder moving down the wall when the bottom of the ladder is 12ft from the wall?
Answer:
Below in bold.
Step-by-step explanation:
The relation between the height of the ladder and distance from the ground is given by Pythagoras Theorem:
h^2 = 13^2 - L^2
h = (169 - L^2)^1/2
Finding the derivative:
dh/dL = 1/2(169 - L^2)^-1/2 * -2L
= -L / (169 -L^2)^1/2
dL/dt = 6
So, dh/dt = dh/dL * dL/dt
= -6 * L/ (169 - L^2)^1/2
= -6 * 12 / (169 - 12^2)^1/2
= -72/5 ft /second
= -14.4 ft/second.
It's negative because the distance from the ground is decreasing.
Kaylee is 1.45 meters tall. At 3 p.m., she measures the length of a tree's shadow to be 39.55 meters. She stands 34.2 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:
Step-by-step explanation:
We can use the ratios of similar triangles to solve this problem. Let's call the height of the tree "h". Then, we have two similar right triangles:
Kaylee's triangle: the height is 1.45 meters, the length of the shadow is 34.2 meters, and the angle between the height and the shadow is theta.
Tree's triangle: the height is h meters, the length of the shadow is 39.55 meters, and the angle between the height and the shadow is also theta.
Using these two triangles, we can set up the following proportion:
h / 39.55 = 1.45 / 34.2
Cross-multiplying, we get:
h * 34.2 = 39.55 * 1.45
Simplifying:
h = (39.55 * 1.45) / 34.2
h = 1.68176
So the height of the tree is approximately 1.68 meters (to the nearest hundredth of a meter).
–6x + 2y =-12
6x + 5y = 117
a. (7, 15) b. (15,9)
c.(-7,-15) d.(-15,-9)
.
I need help
Answer:
B (15,9)
Step-by-step explanation:
There you go
Answer:
a
Step-by-step explanation:
- 6x + 2y = - 12 → (1)
6x + 5y = 117 → (2)
Add the 2 equations term by term to eliminate the x- term
0 + 7y = 105
7y = 105 ( divide both sides by 7 )
y = 15
Substitute y = 15 into either of the 2 equations and solve for x
Substituting into (2)
6x + 5(15) = 117
6x + 75 = 117 ( subtract 75 from both sides )
6x = 42 ( divide both sides by 6 )
x = 7
solution is (7, 15 ) → a
Unit 7: Quantifying Uncertainty: Probability, Binomial, and Normal Distributions
In a mathematics competition, students try
to find the correct answer from five options
in a multiple choice exam of 25 questions.
Alex decides his best strategy is to guess all
the answers.
a. State an appropriate model for the
random variable A = the number of
questions Alex gets correct.
Find the probability that the number of
questions that Alex gets correct is:
b. at most five c at least seven
d no more than three,
e. Write down E(/4) and interpret this
value.
f. Find the probability that Alex scores
more than expected.
g. In the test, a correct answer is awarded
4 points. An incorrect answer incurs a
penalty of 1 point. If Alex guesses all
questions, find the expected value of his
total points for the examination,
h. Four students in total decide to guess all
their answers. Find the probability that
at least two of the four students will get
seven or more questions correct.
a. The appropriate model for the random variable A is the binomial distribution.
b. The probability that Alex gets at most five questions correct can be calculated using the binomial distribution formula.
c. The probability that Alex gets at least seven questions correct can also be calculated using the binomial distribution formula.
d. The probability that Alex gets no more than three questions correct can be calculated using the binomial distribution formula.
e. E(A/4) represents the expected value of A divided by 4, which is the average number of correct answers Alex is expected to get per question.
f. The probability that Alex scores more than expected would depend on the specific values of the expected value and the distribution of the random variable.
g. The expected value of Alex's total points can be calculated by multiplying the expected number of correct answers by 4 and subtracting the expected number of incorrect answers multiplied by 1.
h. The probability that at least two of the four students will get seven or more questions correct would involve calculating the probabilities for each possible combination of students using the binomial distribution and summing them up.
What is probability?
Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event.
a. The appropriate model for the random variable A, the number of questions Alex gets correct, is the binomial distribution.
b. To find the probability that the number of questions Alex gets correct is at most five, we need to calculate P(A ≤ 5) using the binomial distribution formula.
This involves summing up the probabilities of getting 0, 1, 2, 3, 4, or 5 questions correct. The specific values will depend on the probability of guessing a question correctly.
c. To find the probability that the number of questions Alex gets correct is at least seven, we need to calculate P(A ≥ 7) using the binomial distribution formula. This involves summing up the probabilities of getting 7, 8, 9, ..., 25 questions correct. Again, the specific values will depend on the probability of guessing a question correctly.
d. To find the probability that the number of questions Alex gets correct is no more than three, we need to calculate P(A ≤ 3) using the binomial distribution formula. This involves summing up the probabilities of getting 0, 1, 2, or 3 questions correct.
e. E(A/4) represents the expected value of A divided by 4. The expected value is calculated by multiplying each possible outcome by its probability and summing them up. Dividing by 4 scales down the expected value. The interpretation of E(A/4) is the average number of correct answers Alex is expected to get per question.
f. To find the probability that Alex scores more than expected, we would need to compare the actual number of questions he gets correct to the expected value. The probability would depend on the specific values of the expected value and the distribution of the random variable.
g. If a correct answer is awarded 4 points and an incorrect answer incurs a penalty of 1 point, we can calculate the expected value of Alex's total points by multiplying the expected number of correct answers by 4 and subtracting the expected number of incorrect answers and multiply it by 1.
h. To find the probability that at least two of the four students will get seven or more questions correct, we would need to calculate the probabilities for each possible combination of students getting seven or more questions correct (e.g., 2 students, 3 students, 4 students) using the binomial distribution, and sum them up.
a. The appropriate model for the random variable A is the binomial distribution.
b. The probability that Alex gets at most five questions correct can be calculated using the binomial distribution formula.
c. The probability that Alex gets at least seven questions correct can also be calculated using the binomial distribution formula.
d. The probability that Alex gets no more than three questions correct can be calculated using the binomial distribution formula.
e. E(A/4) represents the expected value of A divided by 4, which is the average number of correct answers Alex is expected to get per question.
f. The probability that Alex scores more than expected would depend on the specific values of the expected value and the distribution of the random variable.
g. The expected value of Alex's total points can be calculated by multiplying the expected number of correct answers by 4 and subtracting the expected number of incorrect answers multiplied by 1.
h. The probability that at least two of the four students will get seven or more questions correct would involve calculating the probabilities for each possible combination of students using the binomial distribution and summing them up.
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Denise and her family go out to dinner at a restaurant. The bill is $100. They leave a 20% tip for the server. How much money do they tip?
a.) $12
b.) $20
c.) $10
Sammy went to visit his grandma. He traveled by bus for 24% of his trip. How long was Sammy's trip if he traveled 15 miles by bus?
Where is (-2.5, -2) located on the coordinate plane?
Answer: It is located in quadrant III (3) of the coordinat plain
Step-by-step explanation:
You can use the negative numbers to find their placement. if there are no negative numbers, it’s in quadrant I (1). If there‘s a negative number for the Y-coordinate, then it’s in quadrant II (2). If there are 2 negative numbers, it’s in quadrant III (3). And if there’s a Negative number for the X-coordinate, it’s in quadrant IV (4).
Members of a baseball team raised $1592.50 to go to a tournament. They rented a bus for $844.50 and budgeted $68 per player for meals. Determine the number of players the team can bring to the tournament.
Answer: Assume p to be the number of players, then, the equation which describes this problem is,
844.50+ 68 p = 1592.50844.50+68p=1592.50
68 p = 74868p=748
p = 11p=11.
The number of players, the team can bring to the tournament are 11.
Step-by-step explanation:
Answer: They can bring 11 players to the tournament.
Step-by-step explanation:
$1592.50 - $844.50= $748
Divide $748 by $68, then you will get 11. And 11 will be the answer.