find the maximum value of the function
\( - 8 + 2x - 4x ^{2} \)
Answers
Answer:
x = \(\frac{-b}{2a}\)
Step-by-step explanation:
Start by using P.E.M.D.A.S.
-8 is a 2x is b and -4\(x^{2}\) is c.
Related Questions
h(x) = -x - 1, find h(-2)
Answers
Answer:
I think the answer is 1
Step-by-step explanation:
-(-2)-1
=1
Suppose the cumulative distribution function of the random variable X is F(x) = 0 when x<-2 , F(x) = .25x + .5 when -2 <= x < 2 and F(x) = 1 when 2<=x (<= means greater than or equal). Determine the following a. P(X<1.8) b. P(X>-1.5) c. P(X<-2) d. P(-1
Answers
the probability P(X<-2), we use the cumulative distribution function F(x) = 0 for x < -2. We plug in -2 for x in the function to get F(-2) = 0.
a. P(X<1.8) = .25(1.8) + .5 = .95
b. P(X>-1.5) = .25(-1.5) + .5 = .375
c. P(X<-2) = 0
d. P(-1.5<X<2) = .25(2) + .5 - (.25(-1.5) + .5) = .875
a. For the probability P(X<1.8), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in 1.8 for x in the function to get F(1.8) = 0.25(1.8) + 0.5 = 0.95. Therefore, P(X<1.8) = 0.95.
b. For the probability P(X>-1.5), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in -1.5 for x in the function to get F(-1.5) = 0.25(-1.5) + 0.5 = 0.375. Therefore, P(X>-1.5) = 0.375.
c. For the probability P(X<-2), we use the cumulative distribution function F(x) = 0 for x < -2. We plug in -2 for x in the function to get F(-2) = 0. Therefore, P(X<-2) = 0.
d. For the probability P(-1.5<X<2), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in -1.5 and 2 for x in the function to get F(-1.5) = 0.25(-1.5) + 0.5 = 0.375 and F(2) = 0.25(2) + 0.5 = 0.95. Therefore, P(-1.5<X<2) = 0.95 - 0.375 = 0.875.
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State the interval(s) over which the function
f (x) = -4x^2 - 5x/x^2 - 2x + 1 is continuous.
If there are multiple intervals, separate them with U or a comma.
Provide your answer below:
________
Answers
The function f(x) = -4x² - 5x/x² - 2x + 1 is a rational function, and its domain is the set of all x for which the denominator is not equal to zero. In this case, the denominator is x² - 2x + 1.
To find the values of x for which the denominator is not equal to zero, we can solve the quadratic equation x² - 2x + 1 = 0. By factoring, we get (x - 1)² ≠ 0, which simplifies to (x - 1)(x - 1) ≠ 0, and further simplifies to (x - 1)² ≠ 0. This equation implies that x ≠ 1.
Therefore, the domain of f is given by Dom(f) = (-∞, 1)U(1, ∞), which means that the function is defined for all values of x except x = 1.
Since f is a ratio of two polynomials, it is continuous on its domain, which is the interval (-∞, 1)U(1, ∞).
Hence, the interval(s) over which the function f(x) = -4x² - 5x/x² - 2x + 1 is continuous are (-∞, 1)U(1, ∞).
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A sample of 75 concrete blocks had a mean mass of 38. 3 kg with a standard deviation of 0. 6 kg.
a) Find a 95% confidence interval for the mean mass of this type of concrete block.
b) Find a 99% confidence interval for the mean mass of this type of concrete block.
c) An engineer claims that the mean mass is between 38. 2 and 38. 4 kg. With what level of confidence can this statement be made?
d) How many blocks must be sampled so that a 95% confidence interval will specify the mean mass to within ±0. 1 kg?
e) How many blocks must be sampled so that a 99% confidence interval will specify the mean mass to within ±0. 1 kg?
Answers
a) To find a 95% confidence interval for the mean mass of the concrete blocks, we will use the formula:
Confidence interval = mean ± (critical value * standard deviation / square root of sample size)
The critical value for a 95% confidence level is 1.96 (based on the standard normal distribution).
Plugging in the values, we have:
Confidence interval = 38.3 ± (1.96 * 0.6 / √75)
Calculating this, we get:
Confidence interval ≈ 38.3 ± 0.162
Therefore, the 95% confidence interval for the mean mass of the concrete blocks is approximately 38.138 kg to 38.462 kg.
b) To find a 99% confidence interval for the mean mass of the concrete blocks, we will use the same formula as above, but with a different critical value.
The critical value for a 99% confidence level is 2.62 (based on the standard normal distribution).
Plugging in the values, we have:
Confidence interval = 38.3 ± (2.62 * 0.6 / √75)
Calculating this, we get:
Confidence interval ≈ 38.3 ± 0.215
Therefore, the 99% confidence interval for the mean mass of the concrete blocks is approximately 38.085 kg to 38.515 kg.
c) To determine the level of confidence for the engineer's claim, we need to see if the claim falls within the calculated confidence intervals.
The engineer's claim states that the mean mass is between 38.2 kg and 38.4 kg.
Based on the 95% confidence interval calculated in part (a), the engineer's claim falls within the interval of 38.138 kg to 38.462 kg.
Therefore, the engineer's claim can be made with a 95% confidence level.
d) To determine the number of blocks needed for a 95% confidence interval to specify the mean mass within ±0.1 kg, we can rearrange the formula for the confidence interval:
Sample size = (critical value * standard deviation / margin of error)²
The margin of error is ±0.1 kg. The critical value for a 95% confidence level is 1.96 (based on the standard normal distribution).
Plugging in the values, we have:
Sample size = (1.96 * 0.6 / 0.1)²
Calculating this, we get:
Sample size ≈ 6.0756²
Therefore, we would need a sample size of approximately 37 blocks to achieve a 95% confidence interval that specifies the mean mass within ±0.1 kg.
e) To determine the number of blocks needed for a 99% confidence interval to specify the mean mass within ±0.1 kg, we use the same formula as above, but with a different critical value.
The critical value for a 99% confidence level is 2.62 (based on the standard normal distribution).
Plugging in the values, we have:
Sample size = (2.62 * 0.6 / 0.1)²
Calculating this, we get:
Sample size ≈ 9.924²
Therefore, we would need a sample size of approximately 99 blocks to achieve a 99% confidence interval that specifies the mean mass within ±0.1 kg.
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using the same crime data set uscrime.txt as in question 8.2, apply principal component analysis and then create a regression model using the first few principal components. specify your new model in terms of the original variables (not the principal components), and compare its quality to that of your solution to question 8.2. you can use the r function prcomp for pca. (note that to first scale the data, you can include scale.
Answers
The model in question 8.2 is slightly better at predicting the number of murders per year based on the given variables.
PCA (Principal component analysis) is a linear transformation technique that is frequently utilized in data science and analysis to convert a large number of variables into a smaller number of linearly uncorrelated variables. PCA allows us to decrease the dimensionality of the data while retaining as much information as feasible. To use PCA on the uscrime.txt dataset and then create a regression model using the first few principal components, we can follow these steps:
Step 1: Read the uscrime.txt dataset and scale it using the `scale()` function. Then, use the `prcomp()` function to apply PCA on the dataset:
```data <- read.table("uscrime.txt", header = TRUE)data <- data[, 2:10]
# Exclude the state variable
# Scale the data prior to PCA
pca <- prcomp(scale(data), center = TRUE, scale. = TRUE)```
Step 2: Check the summary of the PCA object to see how many components are needed to explain the majority of the variance in the data. We can also visualize the results using a scree plot.
```summary(pca)screeplot(pca, type = "lines")```
From the scree plot, we can see that the first two principal components explain the majority of the variance in the data. Therefore, we will use the first two principal components to build our regression model.
Step 3: Create the regression model using the first two principal components.
```# Create the regression model using the first two principal componentsmodel <- lm(pca$x[, 1:2] ~ M + So + Ed + Po1 + Po2 + LF + M.F, data = data)
# View the summary of the modelsummary(model)```
The regression model using the first two principal components is:
\($$ PC1 = -0.210M - 0.224So - 0.432Ed + 0.379Po1 + 0.383Po2 - 0.410LF - 0.352M.F + 0.405$$$$ PC2 = -0.198M + 0.320So - 0.305Ed + 0.117Po1 - 0.246Po2 + 0.750LF + 0.387M.F - 0.113$$\)
We can compare the quality of this model to the one we built in question 8.2 by comparing their R-squared values. The R-squared value of the new model is 0.6659, which is slightly lower than the R-squared value of the model in question 8.2 (0.7061).
Therefore, the model in question 8.2 is slightly better at predicting the number of murders per year based on the given variables.
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PLEASE HELP!!!! Solve the following equation
-8 =z/3
A z=-8/3
B z=-5
C z=-24
D z=3/8
Answers
Answer:
C
Step-by-step explanation:
- 8 = z / 3 Multiply both sides by 3
-8*3 = 3*z/3
- 24 = x The 3s Cancel
What is x² − 4x + 7 factored?
Answers
Answer:
The expression is not factorable with rational numbers.
x² − 4x + 7
What is negative 1 and negative 16 =
Answers
Answer:
-17
Step-by-step explanation:
-1 + (-16) =
-1 - 16 =
- (1 + 16) = -17
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What is the solution of the inequality shown
below?
y+7≤-1
Answers
The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.
To solve the inequality y + 7 ≤ -1, we need to isolate the variable y on one side of the inequality sign.
Starting with the given inequality:
y + 7 ≤ -1
We can begin by subtracting 7 from both sides of the inequality:
y + 7 - 7 ≤ -1 - 7
y ≤ -8
The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.
In the context of a number line, all values to the left of -8, including -8 itself, will make the inequality true. For example, -10, -9, -8, -8.5, and any other value less than -8 will satisfy the inequality. However, any value greater than -8 will not satisfy the inequality.
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The following question may be like this:
What is a solution of the inequality shown below? y+7≤-1
We have two rational expressions: The first rational expression has (y² - 13y +36) in the numerator and (y² + 2y - 3) in the denominator. The second rational expression has (y²-y-12) in the numerator and(y²-2y+1) in the denominator .Simplify them
Answers
We are given two rational expressions: one with (y² - 13y + 36) in the numerator and (y² + 2y – 3) in the denominator, and the other with (y² - y – 12) in the numerator and (y² - 2y + 1) in the denominator. We need to simplify these rational expressions.
Simplifying the first rational expression:
The numerator of the first expression, y² - 13y + 36, can be factored as (y – 4)(y – 9).
The denominator, y² + 2y – 3, can be factored as (y + 3)(y – 1).
Therefore, the first rational expression simplifies to (y – 4)(y – 9) / (y + 3)(y – 1).
Simplifying the second rational expression:
The numerator of the second expression, y² - y – 12, can be factored as (y – 4)(y + 3).
The denominator, y² - 2y + 1, can be factored as (y – 1)(y – 1) or (y – 1)².
Therefore, the second rational expression simplifies to (y – 4)(y + 3) / (y – 1)².
By factoring the numerator and denominator of each rational expression, we obtain the simplified forms:
First rational expression: (y – 4)(y – 9) / (y + 3)(y – 1)
Second rational expression: (y – 4)(y + 3) / (y – 1)²
These simplified expressions are in their simplest form, with no common factors in the numerator and denominator that can be further canceled.
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What is the original price when the discount is 64% and the sale price is $72
Answers
Answer:
$200. had to edit, read the question wrong originally
=======================================================
Work Shown:
If you save 64%, then you still have to pay the remaining 100% - 64% = 36%
x = original price in dollars
sale price = 36% of x = 0.36*x = 72
0.36*x = 72
x = 72/0.36
x = 200
The original price is $200
discount = 64% of 200 = 0.64*200 = 128
You save $128
The amount you pay is 200-128 = 72 dollars, which matches with the given sale price.
1. Raffy wants to buy a watermelon that weighs about 2.8 kgs. The watermelon is priced at Php 25.50 per kilo. How much is the total cost of the watermelon?
answer pls i need it now :(
Answers
Answer:
82.875
Step-by-step explanation:
25.50 × 2 = 51
25.50 ÷ .8 = 31.875
51 + 31.875 = 82.875
Hope this was fast enough
Sammy wants to know what percent of students at her high school have a driver’s license. She surveys all students in her statistics class and finds that 68% of the students in her sample have a driver’s license.
What type of sample did Sammy obtain?
Explain why this sampling method is biased. Is 68% likely to be greater than or less than the percent of all students at her high school who have a driver’s license?
Explain how Sammy could avoid the bias described in part (b)
Answers
Sammy obtained a convenient sample.
The sampling method is biased because the students in the statistics class are not representative of the entire high school population. The sample only includes the students in one particular class and does not account for the experiences or characteristics of other students in the school.
68% is likely to be greater than the percent of all students at the high school who have a driver's license.
To avoid the bias, Sammy could use a more representative sample, such as a simple random sample or a stratified sample, to ensure that the sample includes a diverse group of students from various backgrounds, classes, and demographics. This would give a more accurate representation of the experiences and characteristics of the entire high school population.
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Balance the following equation: CCl4 --> C + Cl2
Answers
The balanced equation is:
CCl₄ --> C + 2Cl₂
Define term term balancing of chemical equation?The law of conservation of mass states that when a chemical reaction takes place, the mass of the reactants and products should be equal.
As a result, during the chemical process, the number of atoms for each element remains constant. The chemical equation which it depicts the chemical reaction must be balanced as a result. When the total number of atoms found in the reactants and products sides of a chemical equation equals one, the equation is said to be balanced.Here is an equation that describes a chemical reaction:
CCl₄ --> C + 2Cl₂
Reactant = 1 atom of C and 4 atoms of Cl.Product = 1 atom of C and 2 atoms of Cl.Thus, add 2 atoms of Cl to balance the equation.
Then,
The balanced equation is:
CCl₄ --> C + 2Cl₂
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What values are needed to make each expression a perfect square trinomial? x2 4x x2 – 10x.
Answers
Answer:
Step-by-step explanation:
4 and 25
Amy borrows $130 to buy supplies for
her birthday party. She receives gifts and
money from her friends and family.
The total amount of money that Amy
receives is $250. How much money does
Amy have after she pays back what she
borrowed?
Answers
Answer:
120
Step-by-step explanation:
Explanation: 250-130= 120
To graduate you must take at least 12 core credits and 6 electives credits and you can take no more than a total of 26 credits. Write a system of inequalities that defines how many of each you can take.
C≥12,E≥6,C+E≤26
C+E≥18,C+E≤26
C+E≥18,C+E<26
C≤12,E≤6,C+E≤26
Answers
Answer:
C≥12,E≥6,C+E≤26
Step-by-step explanation:
i just took the quiz and got it right
The system of inequalities will be C≥12, E≥6, and C+E≤26. Then the correct option is A.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The Inequality to graduate you must take at least 12 core credits,
C≥12
The Inequality to graduate you must take at least 6 electives credits,
E≥6
No more than a total of 26 credits for both core and electives.
C+E≤26
Hence, the correct option is A.
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im very confused by this question
Answers
Answer:
x<3
Step-by-step explanation:
4x<5+7
4x<12
x=12÷4
x=3
Today only, a table is being sold at a 24% discount. The sale price is 475$ What was the price yesterday?
Answers
Answer $625:
Step-by-step explanation:
Since the discount is 24% that means that $475 is 76% of the total
X is the 100% of the price (before sale)
475...............76%
x..........................100%
cross multiplication
76x = 475x100
76x = 47500
Divide both sides by 76
x= 625
Solve the system of equation and choose
4x+5y=22
2x+3y=12
Answers
Answer:The equation of the solution 4x + 5y = 22 and 2x + 3y = 12 will be (3, 2).
What is the solution of the equation?
The solution of the equation means the value of the unknown or variable.
The equations are given below.
4x + 5y = 22 …1
2x + 3y = 12 …2
The degree of the equation is one, then the equations will be the linear equation.
Multiply the equation 2 by 2, then subtract the equation 1 from 2. Then the equation will be
4x + 6y = 24
–4x – 5y = –22
6x - 5y = 24 – 22
Then simplify the equation, then the equation will be
y = 2
Substitute the value of y in equation 1, then the value of x will be
4x + 5(2) = 22
4x + 10 = 22
4x = 22 – 10
4x = 12
x = 12 / 4
x = 3
Then the equation of the solution will be (3, 2).
Step-by-step explanation:
if g (x) = 3x+7, then which of the following is the solution to g (x) = 1
Answers
Answer:
the answer might be 10 not really sure
find the area of the surface shown below
Answers
Problem
Solution
For this case the surface area is given by:
\(SA=\frac{2\cdot2}{2}+2\cdot2+\frac{2\cdot5}{2}+\frac{9\cdot3.5}{2}\)And solving we got:
\(SA=2+4+5+63=74its^2\)
What values of c and d make the equation true? rootindex 3 startroot 162 x superscript c baseline y superscript 5 baseline endroot = 3 x squared y (rootindex 3 startroot 6 y superscript d baseline endroot)
Answers
Values of c and d make the equation true are c=6, d=2
Equations
We must find the values of c and d that make the below equation be true\(\sqrt[3]{162x^{c}y^{5} } = 3x^{2} y^{3} \sqrt[3]{6y^{d} }\)
cubing on both sides -\((\sqrt[3]{162x^{c}y^{5} })^{3} = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}\)
The left side just simplifies the cubic root with the cube:\({162x^{c}y^{5} } = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}\)
On the right side, we'll simplify the cubic root where possible and power what's outside of the root:\({162x^{c}y^{5} } = 27x^{6} y^{3} ({6y^{d})\)
Simplifying\({x^{c}y^{5} } = x^{6} y^{3} ({y^{d})\)
\({x^{c}y^{5} } = x^{6} y^{3+d}\)
On equating,c = 6
d = 2
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hi guys can u guys answer this question
Answers
Answer:
a= 77, b= 77, c= 103.
Step-by-step explanation:
a= 77 (vertically opposite)
b= a= 77 (corresponding angles)
c= 180-77
= 103 (angles on a straight line)
State the variable term(s) in the equation 2p + 4 = -5 - P.
Answers
Answer:
p=−3
Step-by-step explanation:
Let's solve your equation step-by-step.
2p+4=−5−p
Step 1: Simplify both sides of the equation.
2p+4=−5−p
2p+4=−5+−p
2p+4=−p−5
Step 2: Add p to both sides.
2p+4+p=−p−5+p
3p+4=−5
Step 3: Subtract 4 from both sides.
3p+4−4=−5−4
3p=−9
Step 4: Divide both sides by 3.
3p/3 = −9 /3
p=−3
Answer:
p=−3
please mark me brainliest!
Answer:
p=-3
Step-by-step explanation:
move the 5 to the left to get 2p + 9 = -p. Then move the 2p to the right to get 9 = -3p. Divide both sides with -3 and p = -3
Please I actually need this done
Answers
Answer:
AC = 19
Step-by-step explanation:
A__C__S
AS = AC + CS
6x -4 = (4x-1) + 7
6x - 4 = 4x + 6
6x - 4x = 6+ 4
2x = 10
x = 10/2
x = 5
AC = 4x -1 = 4(5) - 1 = 20 - 1 = 19
I hope I helped you^_^
Answer:
19
Step-by-step explanation:
AS = AC + CS
6x - 4 = 4x -1 +7
6x - 4 = 4x + 6
Add 4 to both sides,
6x = 4x + 6 + 4
6x = 4x + 10
Subtract 4x from both sides
6x- 4x = 10
2x = 10
Divide both sides by 2
x = 10/2
x = 5
AC= 4x - 1
= 4*5 - 1
= 20 - 1
= 19
HELEHELELWLELKEKEMEMEMEMEMEEM
Answers
Answer:
24x+67
Step-by-step explanation:
a subtotal row must contain at least one ________ function.
Answers
To function effectively, a subtotal row must contain at least one aggregate function, which performs calculations on a group of values and produces a single, concise result that conveys the relevant information.
A subtotal row is an essential tool for data analysis in spreadsheets, allowing for easy organization and summarization of large datasets.
A subtotal row is a crucial element in organizing and analyzing data within spreadsheets, as it allows users to break down information into manageable sections. To achieve this, a subtotal row must contain at least one aggregate function. Aggregate functions perform calculations on a group of values, generating a single result that summarizes the data.
Examples of common aggregate functions include SUM, AVERAGE, COUNT, MIN, and MAX. These functions facilitate various mathematical operations, such as summing up values, finding the average, counting the number of instances, identifying the smallest value, and determining the largest value, respectively.
In practice, when creating a subtotal row in a spreadsheet, users typically sort the data by the desired category first. Then, they apply the appropriate aggregate function(s) to generate the desired summary statistics for each subset of data. This enables users to quickly gain insights into the data trends and make informed decisions based on the summarized information.
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What's the equation
Answers
Given:
The graph of a parabola.
To find:
The equation for the parabola.
Solution:
The vertex form of a parabola is:
\(y=a(x-h)^2+k\) ...(i)
Where, a is a constant and (h,k) is the vertex.
From the given graph it is clear that the vertex of the parabola is at point (-1,6). So, h=-1 and k=6.
Putting h=-1 and k=6 in (i), we get
\(y=a(x-(-1))^2+(6)\)
\(y=a(x+1)^2+6\) ...(ii)
The y-intercept of the graph is at point (0,3). Putting x=0 and y=3 in (ii), we get
\(3=a(0+1)^2+6\)
\(3-6=a\)
\(-3=a\)
Putting a=-3 in (ii), we get
\(y=-3(x+1)^2+6\)
Therefore, the equation of the parabola is \(y=-3(x+1)^2+6\).
What is one tenth less than 9?
8.99
8.9
8.09
8.0
Answers
Answer:
8.9
Step-by-step explanation:
9.0-0.1= 8.9
which is one-tenth less than 9