The value of 'p' obtained by completing the square is √5 - 2.
Define the term completing square?Completing the square is the process of engineering the quadratic equation to produce a perfect square by adding and subtracting both from sides.The given equation in the question is-
p² + 4p = 1
4 divided by half is 2, but 2 squared is 4, therefore
p² + 4p + 4 = 1 + 4
Putting that part of "b" between parenthesis is the simplest method to describe it at this point.
(p + 2)² = 5
The result of multiplying (p + 2)(p + 2) is p² + 4p + 4.
A square root from both sides is now calculated.
p + 2 = √5
p = √5 - 2
Thus, the value of 'p' obtained by completing the square is √5 - 2.
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The correct question is-
Solve the equation p² + 4p = 1 by completing square.
write the equation for the parabola that has its x-intercepts at (-2, 0) and (4, 0) and its y-intercept at (0, 4).
The equation for the parabola is y = (5/3)(x + 2)(x - 1.2)
What is equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about mathematical equations.
How do we solve equations?Remove parentheses from each side of the equation and combine similar terms to make it simpler.
To separate the variable term on one side of the equation, use addition or subtraction.
To find the variable, use division or multiplication.
y = A [x - (-2)] (x - 1.2)
y = A(x + 2)(x - 1.2)
At the y-intercept,
-4 = A(0 + 2)(0 - 1.2)
-4 = -2.4A
A = 4/2.4 = 5/3
y = (5/3)(x + 2)(x - 1.2)
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Put the steps in order that are used to solve the following systems of equations by substitution.
-7x - 2y
2y
= x= 2 (-4) +11 → x = 3
x
-
=
= - 13
11
= x - 2y = 11 → x = 2y + 11
=y=-4
= -7 (2y + 11) - 2y = -13
= (3,-4)
= -16y = 64
= -16y - 77 = -13
= -14y-77-2y = -13
The steps that are used to solve the above equation by substitution include the following:
1.) X = 11 + 2y
2.) -7 ( 2y + 11) -2y = -13
3.) -14y -77- 2y = -13
4.) -16y - 77 = -13
5.) -16y = 64
6.) y= -4
7.) X = 2(-4) + 11 --> X = 3
8.) (3, -4)
What is a substitution equation?A substitution equation is defined as the type of equation that involves solving the equation for one variable, and substituting the value of the variable in the other equation.
The given equation is as follows;
-7x -2y = -13
X - 2y = 11.
To solve for X the following is done;
X = 2y + 11
Substitute X = 2y + 11 into equation 1
-7 ( 2y + 11) -2y = -13
Multiple out to open the brackets;
= -14y -77- 2y = -13
= -16y - 77 = -13
= -16y = 64
= y= -4
Then substitute y = -4 into equation two as follows;
X = 2(-4) + 11
X = 3
Therefore, y = -4, while X = 3 that is ( 3,-4)
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juliet rented a car for one day from a company that charges $80 per day plus $0.15 per mile driven. if she was charged a total of $98 for the rental and mileage, for how many miles of driving w
Juliet was charged $18 for driving 120 miles.
Given,
The rent of car per day = $80
The charge for per miles driven = $0.15
Juliet was charged a total of $98 for the rental and mileage.
We have to find the total miles of driving;
Here,
Charge for miles driven = Total charge - Rent of car for a day
Charge for miles driven = 98 - 80
Charge for miles driven = $18
Now,
Total miles driven = Charge for miles driven / Charge for one mile
Total miles driven = 18/0.15
Total miles driven = 120
That is,
Juliet was charged $18 for 120 miles of driving.
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Many cars have keyless entry. To open the lock, you may press a 5-digit code on a set of buttons like that illustrated. The code may include repeated digits like 11433 or 55512. 1-2 3-4 5-67-8 9-0 a) How many different 5-digit codes can be made using the 10 digits if repetition is permitted?
Answer:
You can make up to "9" different 5-digit codes
which technique is likely to discover a value that is 10x larger than the next highest value in a dataset of 500,000 records? group of answer choices basic statistical tests. visual inspection. advanced testing techniques. auditing a sample.
The correct option is (a). basic statistical tests the technique is likely to discover a value that is 10x larger than the next highest value in a dataset of 500,000 records is basic statistical tests.
Statistical assessments are utilized in speculation trying out. They may be used to: decide whether a predictor variable has a statistically substantial relationship with an outcome variable. estimate the distinction between or more groups.
Two main statistical techniques are used in data analysis: descriptive facts, which summarize records of the usage of indexes along with suggestions and median and every other is inferential facts, which draw conclusions from records of the usage of statistical assessments including pupil's t-take look at.
In fact, there are foremost kinds of assessments: parametric and non-parametric. each sort of assessment is used to make inferences about a populace based on a sample. The difference between the 2 styles of tests lies within the assumptions that they make about the records.
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the board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 4.00 minutes. to make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 42 randomly selected calls. the mean wait time was calculated to be 4.14 minutes. assuming the population standard deviation is 0.55 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 4.00 minutes with a 98% level of confidence?
Answer of the following questions for given mean and standard deviation along with sample size are:
a. Null hypothesis , H₀: μ = 4.00
Alternative hypothesis, H₁ : μ > 4.00
b. Value of test statistic is 1.647
c. Conclusion is no evidence to conclude mean wait time for customer is longer than 4.00 minutes.
As given in the question,
Wait time for customer is at most 4.00 minutes
a. Null hypothesis is given by
H₀: μ = 4.00
Mean time is not exceeding the requirement
Alternative hypothesis is given by:
H₁ : μ > 4.00
b. Value of test statistic is given by :
([tex]\bar{x}[/tex] - μ₀) ÷ ( s/√n )
Sample mean [tex]\bar{x}[/tex] = 4.14
Population mean μ₀ = 4.00
Standard deviation 's' = 0.55 minutes
Sample size 'n' = 42
Substitute the value in the formula we get,
(4.14 - 4.00) ÷ (0.55/ √42)
= 0.14 / (0.55/ 6.5)
=0.14/ 0.085
= 1.647
c. α = 1 - 98%
= 1 - 0.98
= 0.02
Decision value limit :
Reject H₀ ; if P value < α
Using table ,
P value = P(Z < 1.647)
= 0.04997
⇒P value = 0.04997
0.04997 > 0.02
Here P value > α
Fail to reject Null hypothesis .
Therefore, from the given standard deviation and mean conclusion is that there is no sufficient evidence to prove that mean wait time for customers is longer than 4.00.
The complete question is:
The board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 4.00 minutes. to make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 42 randomly selected calls. the mean wait time was calculated to be 4.14 minutes. assuming the population standard deviation is 0.55 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 4.00 minutes with a 98% level of confidence?
1. State the null and alternative hypotheses for the test.
2. Compute the value of the test statistic.
3. Draw a conclusion and interpret the decision.
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2. Which equation has a graph perpendicular to the graph of 7x = 14y-8? (1 point)
Oy=-2x - 7
Oy=-=x+4
2
Oy= 2x+1
2
Oy = 2x +9
Answer:
Step-by-step explanation:
the 2nd one
9. identify two different conditions under which the regression line should not be used to make predictions.
Extrapolation is the process of making predictions outside the range of numbers by using the regression line.
Explain the term regression line?The assessment of the line that depicts the actual, but unidentified, linear correlation is called a regression line. When the values of the explanatory variable is known, the regression line's equation is applied to predict (as well as estimate) the quantity of the response variable.The linear regression model is predicated on the following premises: Linearity: X and also the mean of Y have a straight line connection. Homoscedasticity: For every value of X, the variance of the residual is the same. Independent of one another: Observations are separate from one another.Extrapolation refers to using the regression line to produce predictions outside of the data's range.
Thus,despite the correlation maybe having a linear shape within the range being observed, this method can be risky because it's possible that it wouldn't hold true over a wider range.
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At the beginning of 1st grade, Steve is initially able to spell 10 words. He is planning to learn 3 new words each week. How many weeks will it take him to
learn to spell a minimum of 46 words?
Answer:
15 weeks.........
Step-by-step explanation:
3×15=45
What is the solution to square root of 7x - 4 = 2 square root of x
The square root √(7 · x - 4) = 2 has a solution for the variable x is 8 / 7.
How to find the solution to a square root
In this problem, we find a square root whose solution for the variable x has to be found solely by algebra properties. First, write the radical equation:
√(7 · x - 4) = 2
Second, elevate to the square of the expression:
7 · x - 4 = 4
Third, clear the variable x by algebra properties:
7 · x = 8
x = 8 / 7
The solution to the square root is equal to 8 / 7.
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4(4m-3)-1(m-5)=-52
solve for M
Answer:
m = -3
Step-by-step explanation:
4(4m - 3) - 1(m - 5) = -52
Distribute both expressions (don't forget that the 1 is -1, so distribute -1.)
16m - 12 - m + 5 = -52
Add like terms
15m - 7 = -52
Add 7 on both sides
15m = -45
Divide by 15 on both sides
m = -3
how is 27.25 divided by 5 = 5.05. Doesn't it equal 5.45
Answer:
Yes you are right
Step-by-step explanation:
It equals 5.45
how do I compare 6.098 and 6.908
6.908 is greater than 6.098 as the second digit from the left is greater.
What is rounding off of numbers?We round off numbers to make them easier to remember and it also keeps its value approximately to the place it has been rounded off.
To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.
Given, are two numbers 6.098 and 6.908.
Now, starting from left both the numbers have the same digit so we can't
differentiate.
The digit after the decimal place to the first number is 0 and on the second it is 9 so definitely, the second number is greater.
∴ 6.098 < 6.908.
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Which expressions are equivalent to -5x - 15 + 25x - 30? Choose ALL that apply. −5(2 − 3+52 – 6) −5(2 – 5x + 9) −5(2+3 – 5x – 6) -5(6x - 9) -5(-4x+9) −5(2+3–52+6)
The correct expression that is equivalent to the algebraic expression -5x - 15 + 25x - 30 is -5(-4x + 9).
How to determine the equivalent expressionWe shall simplify the given algebraic expression by carrying out basic mathematics operations as follows;
Given: -5x - 15 + 25x - 30
we group like terms together
25x - 5x - 15 - 30
20x - 45
the number 5 is a common factor of 20x and 45, so we have that;
5 × 4x - 5 × 9
by factoring out 5
5(4x - 9)
also;
5(4x - 9) = -5(-4x + 9)
Therefore, -5(-4x + 9) is an equivalent expression to the algebraic expression -5x - 15 + 25x - 30
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can somone please help me with this i kmnow its alot but im begging you
Answer: The answers to the first page
Step-by-step explanation:
Question 1
Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.
6
−48
>x
Divide −48 by 6 to get −8.
−8>x
Swap sides so that all variable terms are on the left-hand side. This changes the sign direction.
x<−8
Question 2
−3x+8>11
Subtract 8 from both sides.
−3x>11−8
Subtract 8 from 11 to get 3.
−3x>3
Divide both sides by −3. Since −3 is negative, the inequality direction is changed.
x<
−3
3
Divide 3 by −3 to get −1.
x<−1
Question 3
15x+60>240
Subtract 60 from both sides.
15x>240−60
Subtract 60 from 240 to get 180.
15x>180
Divide both sides by 15. Since 15 is positive, the inequality direction remains the same.
x>
15
180
Divide 180 by 15 to get 12.
x>12
Question 4
3rd answer choice
Question 5
First, let's calculate how many miles he has left.
80 - 14 = 66
Now, to figure out how many miles a day in 6 days, divide.
66/6 = 11
Xavier should bike 11 miles on each of the 6 remaining days.
What is the value of the expression when a = 3 and b = 5?
3a+b−4
Responses
4
4
7
7
10
10
34
34
Answer: It's ten...please give me brainliest. I'm begging you.
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
a = 3; b = 5
3a + b − 4 =
= 3(3) + 5 - 4
= 9 + 5 - 4
= 14 - 4
= 10
in multiple regression analysis, the correlation among the independent variables is termed . select one: a. homoscedasticity b. linearity c. multicollinearity d. adjusted coefficient of determination
In multiple linear regression analysis, the correlation among independent variables is termed multicollinearity i.e. option C.
Definition:
a) Homoscedasticity: Homoscedasticity, also known as homogeneity of variances, is the presumption that variations in various groups being compared are equivalent or comparable.
b) Linearity: A mathematical relationship (function) that can be graphically represented as a straight line is said to be linear. Proportionality and linearity are closely linked concepts.
c) Multicollinearity: Multiple independent variables in a model that are correlating from a statistical concept known as multicollinearity.
d) Adjusted Coefficient of Determination: The number of variables in a data collection is taken into account when calculating the adjusted coefficient of determination (also known as adjusted R-squared). Additionally, it penalizes you for any points that deviate from the model.
Hence, the required choice is Option C.
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parker travels the country speaking to college students about the importance of staying in school. he analyzes sophomores in particular. what do college sophomores represent?
The college sophomores analysed by Parker represent demographics.
Demographics is defined as the statistics concerned with characteristics and population of any particular group. Inspecting the question, we see the Parker travels multiple countries focussing on sophomores.
Hence, sophomores are specific population being studied thus representing demographics. They will be represented as statistical data. There are multiple examples of demographics characteristics such as age, religion, gender, ethnicity, disability status, home ownership, income, education, psychiatric diagnosis and many others.
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a cylinder with open top with radius r and height h has surface area 8 cm2 . find the largest possible volume of such a cylinder.
If the surface area of the cylinder is 8cm , then the largest possible volume of such cylinder is (16/3)√(2/3π) cubic units .
In the question ,
it is given that ,
the cylinder is an open top ,
given that surface area = 8cm² ,
So , the surface area is = 2πrh + πr²,
8 = 2πrh + πr²
So , h = (8 - πr²)/2πr ,
the volume of the cylinder is (V) = πr²h ,
Substituting the value of h ,
we get ,
V = (8r - πr³)/2,
to find the largest volume , we differentiate it with respect to "r" and equate to 0 ,
we get ,
(8r - πr³)/2 = 0
On Simplifying we get ,
r = √(8/3π) ,
the volume is maximum when r = √(8/3π) ,
So , Volume is = ( 8(√8/3π) - π√(8/3π)³)/2
V = 4(√(8/3π)) - (4/3)(√(8/3π))
V = (8/3)√(8/3π)
V = (16/3)√(2/3π) cubic units .
Therefore , the maximum volume is (16/3)√(2/3π) cubic units .
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There are 16 squares and 4 circles. What is the simplest ratio of circles to total shapes?
Answer: 4:1
Step-by-step explanation:
We know that there are 16 squares in 4 circles, so the ratio is 16:4 and we can simplify this ratio by dividing by 4 which equal 4:1
If you can please give me a Brainliest, I only need 3 more to become an Ace, thank you!
Plot the points (-4, 6) and (5,3) and find the slope.
Answer:
-1/3
Step-by-step explanation:
3-6/5-(-4) = -3/9
simplify -3/9
-1/3
Please find x and y! And explain!
Answer:
x = 10
y = 15
Step-by-step explanation:
Start with y.
The smaller triangle has a right angle and two congruent legs.
Since the legs are congruent, then the opposite angles are also congruent.
The measures of the 3 angles of the right triangle are:
3y, 3y, 90
The sum of the measures of the angles of a triangle is 180°.
3y + 3y + 90 = 180
6y + 90 = 180
6y = 90
y = 15
The larger triangle has 2 congruent sides. The opposite angles are congruent. Each of the congruent angles measures 2x + 3y. The angle above measures 50°.
2x + 3y + 2x + 3y + 50 = 180
4x + 6y + 50 = 180
4x + 6y = 130
We know from above that y = 15.
4x + 6(15) = 130
4x + 90 = 130
4x = 40
x = 10
A researcher developing a regression equation to predict income in thousands of dollars from age (A) and educational status (%) found a significant interaction between age and educational status (X). Educational status is a dummy variable with 0 = high school or less and 1 = some education beyond high school Given the equation = 14.2 + 0.5 1 + 1.7X2 + 0.1X3 + e, what is the predicted income for a 43-year- old who left school after the 10th grade? $35,700 $37.400 $34,000 $35,800
The predicted income for a 43-year- old who left school after the 10th grade is in option (A) i.e. $35,700.
Given that:
Educational status is a dummy variable with 0 = high school or less and 1 = some education beyond high school
Regression equation = 14.2 + 0.5 X1 + 1.7X2 + 0.1X3 + e
X1 => Age; X3→ (0 if high school or less and 1 if some education beyond high school)
X2 => (X2 * X3)→ (0 if high school or less and X1 if some education beyond high school)
Given: X1 = 43, X2 and X3 = 0
Putting these values in the below equation.
y = 14.2 + 0.5 X1 + 1.7X2 + 0.1X3 + e
y = 14.2 + (0.5 x 43) + 1.7 x 0 + .1 x 0 + e
y = 14.2 + (0.5 x 43) + 0 + 0 + e
y = 14.2 + 21.5 + e
y = 35.7 + e
The value of e can be neglected as it is a constant value.
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>) The Johnsons set aside money in their budget for food for their anniversary party. They spent $320 but had set aside 25% more than that. How much money did the Johnsons set aside in their budget for food for the party?
Answer:
$400
Step-by-step explanation:
y= 320×(1+0.25)=400
Find all solutions to the equation b² = 13
Answer: The correct answer is b = √13 or b = −√13
Step-by-step explanation:
When factoring squared variables or numbers, use the square root
b^2 = 13
Take the square root of both sides
√b^2 = √13
b = √13 or b = −√13
Use point-slope form to write the equation of a line that passes through the point
(-1, 3) with slope-11/6
Answer:
y-3= -11/6(x+1)
Step-by-step explanation:
y-3 = -11/6(x-(-1)
y-3 = -11/6(x+1)
Can someone please explain how to solve this type of equation?
Answer:
n = 15
Step-by-step explanation:
the triangles are similar so the correspondent sides are proportional
2: 5 = 6 : n
n = 6 x 5 /2
n = 3 x 5
n = 15
h(x) =(√x + 1)(√x - 3)
mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. a recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. the recruiting office randomly surveys 46 entry level mechanical engineers and 52 entry level electrical engineers. their mean salaries were $46,100 and $46,900, respectively. their standard deviations were $3450 and $4230, respectively. conduct a hypothesis test at the 5% level to determine if you agree that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary. let the subscript m = mechanical and e = electrical. i. In words, state what your random variable X- Xe represents ii. State the distribution to use for the test. (Enter your answer in the form z or taf where df is the degrees of freedom. Round your answer to two decimal places.) iii. What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) iv. What is the p-value? (Round your answer to four decimal places.) v. Alpha (Enter an exact number as an integer, fraction, or decimal.)
Answer:
i. X represents the difference between the mean entry-level mechanical engineering salary and the mean entry-level electrical engineering salary.
ii. t distribution with df = 96
iii. t = -2.38
iv. p-value = 0.0190
v. Alpha = 0.05
i. The random variable X - Xe represents the difference in mean salaries between mechanical engineering (X) and electrical engineering (Xe).
ii. We used the t-distribution for the test due to unknown population standard deviations and relatively small sample sizes.
iii. The calculated test statistic is -2.1095.
iv. The degrees of freedom for the t-distribution are approximately 113242.
v. The p-value associated with the test statistic and degrees of freedom is approximately 0.0001.
i. The random variable X - Xe represents the difference in mean salaries between mechanical engineering (X) and electrical engineering (Xe).
ii. We will use the t-distribution for the test since the population standard deviations are unknown, and the sample sizes are relatively small (less than 30).
iii. The test statistic for this hypothesis test is calculated as:
[tex]t = (X - Xe) / \sqrt(s_m^2 / n_m) + (s_e^2 / n_e))}[/tex]
Where:
X = sample mean for mechanical engineering
Xe = sample mean for electrical engineering
Sm = standard deviation for mechanical engineering
Se= standard deviation for electrical engineering
nm = sample size for mechanical engineering
ne = sample size for electrical engineering
t = (46100 - 46900) / √(3450² / 46) + (4230² / 52))
= -800 / √(3450² / 46) + (4230² / 52))
= -800 / 379.4303
= -2.1095
iv.
Calculating the degrees of freedom:
df = (3450² / 46 + 4230² / 52)² / ((3450² / 46)² / (46 - 1) + (4230² / 52)² / (52 - 1))
= (119023.913 + 180714.2308)² / ((119023.913)² / 45 + (180714.2308)² / 51)
= 113242.1436
The degrees of freedom are approximately 113242.
Now, we need to find the p-value associated with the test statistic and degrees of freedom.
We can use a t-distribution table to look up the p-value.
Since the test is one-tailed and the test statistic is negative, we will look up the p-value in the left tail of the t-distribution with the given degrees of freedom.
Assuming the p-value is less than 0.0001, we can state that the p-value is approximately 0.0001.
v. To conduct a hypothesis test at the 5% level to determine if you agree that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.
So, the significance level (alpha) is given as 5%.
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Which number is a composite number?
A.11
B.21
C.31
D.41
Answer:
B. 21
Step-by-step explanation:
Composite numbers have more than two factors.
Answer: 21
Step-by-step explanation: