Answer:
He did not check for extraneous solutions.
Step-by-step explanation:
He solved the equation correctly and obtained solutions -2 and -5, but there is one final step he did not do.
Every time you square both sides of an equation to solve it, you must check for extraneous solutions. If he did, he would have eliminated x = -5.
Answer: He did not check for extraneous solutions.
Add 6 and 8 the add p
Answer:
Step-by-step explanation:
6 + 8 + p = 14 + p
Answer: 14+p
Step-by-step explanation: We have to add these numbers-
6 + 8 + p
14+p
(Since we don't know the value of p this is how far we can simplify )
Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.a) 91.69 < μ < 98.31b) 92.95 < μ < 97.05c) 91.68 < μ < 98.32d) 92.03 < μ < 97.97
Answer: c) 91.68 < μ < 98.32
Step-by-step explanation:
Let μ be the mean score of all students.
Let [tex]\overline{x}[/tex] represents the sample mean score.
As per given , we have
Sample size : n= 30
Sample mean : [tex]\overline{x}=95[/tex]
Sample standard deviation: [tex]s=6.6[/tex]
Significance level [tex]\alpha=0.01[/tex]
Now, Confidence interval of mean when population standard deviation is unknown is given by :-
[tex]\overline{x}\pm t_{\alpha/2, df}\dfrac{s}{\sqrt{n}}[/tex]
Degree of freedom = n-1 = 29
Critical two-tailed t-value : [tex]t_{0.01/2,29}=t_{0.005,29}=2.756[/tex] [By students' t distribution table]
Confidence interval of mean will be:
[tex]95\pm (2.756)\dfrac{6.6}{\sqrt{30}}\\\\=95\pm (2.756)\dfrac{6.6}{5.47722557}\\\\=95\pm (2.756)(1.205)\\\\=95\pm 3.32\\\\= (95-3.32, 95+3.32)\\\\=(91.68,\ 98.32)[/tex]
i.e. a 99% confidence interval for the mean score of all students : 91.68 < μ < 98.32
So correct option is c) .
Find the value of x in each case:
Answer:
[tex] x = 18 [/tex]
Step-by-step explanation:
Given:
Angle ABC = 2x
Angle CDE = 8x
Required:
Value of x
SOLUTION:
Line AB is parallel to line CD, therefore, angle ABC and angle BCD are alternate interior angles. Alternate interior angles are equal. Thus:
Angle ABC = Angle BCD = 2x
Since, line BC is parallel to line DE, angle BCD and angle CDE are consecutive interior angles.
Consecutive interior angles are supplementary, therefore:
Angle BCD + Angle CDE = 180°
[tex] 2x + 8x = 180 [/tex]
Use this equation to solve for x
[tex] 10x = 180 [/tex]
Divide both sides by 10
[tex] \frac{10x}{10} = \frac{180}{10} [/tex]
[tex] x = 18 [/tex]
How many thousands are in 30 hundreds
Answer:
3
Step-by-step explanation:
30 hundreds = 30*100 which = 3000 and 3000/1000 = 3
Answer:
3
Step-by-step explanation:
30x100=3000 is the answer to solving your problem
How many different letter permutations, of any length, can be made using the letters M O T T O (For instance, there are 3 possible permutations of length 1.)
Answer:
89
Step-by-step explanation:
Given that
2 O, 2 T and 1 M
Now based on this, the following ways are there
1
Three ways i.e. {M,T,O}
2
XX or XY
XX in 2C1 = two ways i.e. {OO or TT}
XY in 3C2 × 2! = six ways
3
XXY or XYZ
XXY in 2C1 × 2C1 × 3! ÷ 2! = twelve ways
XYZ in 3C3 × 3! = six ways
4
XXYY or XXYZ
XXYY = 4! ÷ (2! × 2!) = six ways
XXYZ in 2C1 × 4! ÷ 2! = twenty four ways
5
= 5! ÷ (2! ×2!)
= 120 ÷ 4
= 30
Therefore, the total is
= 3 + (2 +6)+ (12 +6) + (6 +24) + 30
= 89
There are 30 different letter permutations.
The word is given as:
MOTTO
From the given word, we have the following parameters:
[tex]n = 5[/tex] --- the number of characters in the word[tex]T = 2[/tex] --- the number of times letter T appears[tex]O = 2[/tex] --- the number of times letter O appearsThe number of different (d) letter permutation is then calculated as:
[tex]d = \frac{n!}{T!O!}[/tex]
This gives
[tex]d = \frac{5!}{2!2!}[/tex]
Evaluate each factorial
[tex]d = \frac{120}{2 \times 2}[/tex]
Evaluate the product of 2 and 2
[tex]d = \frac{120}{4}[/tex]
Divide 120 by 4
[tex]d = 30[/tex]
Hence, there are 30 different letter permutations.
Read more about permutations at:
https://brainly.com/question/11732255
find the minimum of c=x+3y
Answer:
14
Step-by-step explanation:
The objective function C=x+3y is the same as one of the constraining boundaries, x+3y≥14. Hence the minimum value of C is constrained to be 14.
-5(y + 1) + 6y
Need help
Answer:
1y - 5
Step-by-step explanation:
Remember to follow PEMDAS. Simplify the expression.
PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
First, distribute -5 to all terms within the parenthesis:
-5(y) = -5y
-5(1) = -5
Next, combine like terms:
-5y + 6y - 5
(-5y + 6y) - 5
1y - 5
1y - 5 is your answer.
~
When you look into a mirror, you see your reflection. Explain how this relates to reflections in
geometry.
State whether the data described below are discrete or continuous, and explain why.
The number of car accidents on a given stretch of highway each year
Choose the correct answer below.
O A. The data are continuous because the data can take on any value in an interval.
OB. The data are discrete because the data can take on any value in an interval.
C. The data are continuous because the data can only take on specific values.
D. The data are discrete because the data can only take on specific values.
Answer: D. The data are discrete because the data can only take on specific values.
Step-by-step explanation:
Discrete data refers to data that has a specific value in a specific period and so can be counted as opposed to continuous data that cannot be counted as it goes on to infinity. An example of continuous data would be the height of students in a class. This is continuous because a person's height could be 1.02325845...... metres.
The number of car accidents on a particular stretch of highway can be counted and the data can only take on a specific value thereby making it discrete data.
In this exercise we have to use the knowledge of distance to understand which the best alternative corresponds to car accidents, in this way we find that:
Letter D. The data are discrete because the data can only take on specific values.
Discrete information in visible form refers to data that bear a distinguishing value fashionable a distinguishing period accordingly can be check in order as opposite to continuous information in visible form that cannot be deem as it continue to infinity.
An instance of constant data hopeful the height of person actively learning fashionable a class. This is constant cause a person's crest could be 1.02325845 metres.
The number of vehicle driven on streets accidents in contact a particular stretch of heavily traveled maybe have importance and the data can only oppose a particular financial worth by that making it discrete information in visible form.
See more about distance at brainly.com/question/989117
FIRST TO ANSWER GETS BRAINLYEST!!!!!!
Answer:
m ≈ 3
Step-by-step explanation:
3.53631284916 x 10^3 ≈ 3 x 10^3
A pink crayon is made with 12 ml
Answer:
ok
Step-by-step explanation:
How is completing the square beneficial ? Edge 2020 key words
What is the answer for n-29=-53
Answer:
n=-24
Step-by-step explanation:
Answer:
n =-24
Step-by-step explanation:
[tex]n-29=-53[/tex]
Collect like terms and simplify
[tex]n =-53+29\\\\n =-24[/tex]
a turtle crawled at a speed of 1.2 meters per minute for nine minutes how far did the turtle crawl
Answer:
10.8 meters
Step-by-step explanation:
1.2 times 9 minutes= 10.8
Answer:
10.8 meters
Step-by-step explanation:
9 * 1.2 = 10.8
What is (-9)+9 simplified
Answer:
the answer is zero
Step-by-step explanation:
-9+9=0
To which graph does the point (8;-2) belong?
quadrant 4
.................
Answer:
Quadrant 4
Step-by-step explanation:
In Quadrant 4 the x-axis is positive (+) and the y-axis is negative (-). Here is the point plotted on a coordinate grid to help you understand better.
Hope this helps :)
Pt. 1 The result of adding a complex number to its conjugate is a.- a whole number b.-an integer, c.- a real number, d.- a pure imaginary number Pt. 2 And the result of subtracting a complex number from its conjugate is a.- a whole number, b.-an integer, c.- a pure imaginary number, d.- a real number
Answer:
Step-by-step explanation:
A complex number is a number that has both real and imaginary part. An example of a complex number is z = x+iy where x is the real part and y is the imaginary part.
If z = x+iy, the conjugate of z₁ will be x-iy
adding the complex number to its conjugate will give;
P = z+z₁
P = x+iy +(x-iy)
open the parenthesis
P = x+iy+x-iy
collect like terms
P = x+x+iy-iy
P = 2x
We can see that the resulting value does not contain the imaginary number i, hence the result is a real number.
Hence the result of adding a complex number to its conjugate is a REAL NUMBER
Taking the difference;
P = = z-z₁
P = x+iy -(x-iy)
open the parenthesis
P = x+iy-x+iy
collect like terms
P = x-x+iy+iy
P = 0+2iy
P = 2iy
We can see that the resulting value contains the imaginary number i, hence the of taking their difference is a complex number.
Hence the result of subtracting a complex number from its conjugate is an IMAGINARY NUMBER
Which of the following is irrational?
6
25
0.16
900
Answer:
0.16
Step-by-step explanation:
Give the Domain and Range of H={(-2,-3),(5,9),(5,-2)}
Write your answer using set notations
The domain is the set of possible x values or inputs. We list each unique x value once (ignoring any repeats)
The range is the set of possible y outputs. Convention is to sort the values from smallest to largest.
This relation is not a function because the x value x = 5 corresponds to multiple y values.
Three and a half more than a number
Answer:
x + 3.5
Step-by-step explanation:
You are adding
hopefully this helps you:)
How do you define mathematics?
Answer:
The overall group of sciences that study numbers, shapes and their relationships. An example of math is arithmetic, the study of addition, subtraction, multiplication and division.
Write the quadratic equation whose roots are -4 and 4 and whose leading coeffiecient is 3. Use the letter X to represent the variavble.
Answer:
3x^2 - 48 = 0
Step-by-step explanation:
The roots of a quadratic equation whose roots are -4 and 4, means that valid solutions for the quadratic equation are -4 and 4.
The two forms we know for the quadratic equation are the factored binomials:
(ax + cy)(bx + dz) = 0
and the full equation
ax^2 + bx + c = 0
We will start with the factored form:
(x + 4) ( x - 4) = 0
Note that if we solve this, we get the roots: x + 4 = 0 ==> -4 && x - 4 = 0 ==> 4
Now we apply foil to get the unfactored form:
(x + 4) (x - 4) = 0
x * x + x * -4 + 4 * x + 4 * -4 = 0
x^2 + -4x + 4x + -16 = 0
x^2 - 16 = 0
And now we want the leading coefficient to be 3.
3x^2 - 16 = 0
This looks like what we want; however, now with the leading 3, our solutions are no long +4 and -4. So, we need to re-evaluate.
Going back to the binomials with the idea of a leading 3, let's rewrite them to still give us the solutions 4 and -4, but with the 3 included:
(3x + 12) (x - 4) = 0
Note, we simply multipled one binomial by 3 to maintain the roots of the original, but also incorporate the leading 3.
3x + 12 = 0 x - 4 = 0
3x = -12 x = 4
x = -4
So now, we simply apply foil to this new equation of binomials to get our final quadratic equation:
(3x + 12) (x - 4) = 0
3x * x + 3x * -4 + 12 * x + 12 * -4 = 0
3x^2 + -12x + 12x + -48 = 0
3x^2 - 48 = 0
This is our quadratic equation we wish to use.
Note, we could have gotten this same equation by simply multiplying the original (x^2 - 16) = 0 by 3.
Cheers.
Help me please i dont know what to write
Answer:
Decomposers in a food web are organisms that break down dead or decaying organisms and turn them into simpler, inorganic materials, making nutrients available for primary producers. A rotten fruit is not completely wasted because it will go back into the dirt for a producer to use, and the food chain continues.
Hope this helps!
For the function f(x) = 16x^3 - x, make a table of slopes of secant lines and make a conjecture about the slope of the tangent line at x = 1. Complete the table. (Round the final answer to three decimal places as needed. Round all intermediate values to four decimal places as needed.) An accurate conjecture for the slope of the tangent line at x = 1 is (Round to the nearest integer as needed.)
Complete Question
The complete question is shown on the first uploaded image
Answer:
Interval Slope of secant lines
[1,2] 113.000
[1, 1.5] 75.000
[1, 1.1 ] 51.960
[1, 1.01] 47.482
[1, 1.001] 47.048
Step-by-step explanation:
From the question we are told that
The function is [tex]f(x) = 16x^3 -x[/tex]
Now considering the intervals
For [1, 2]
The slopes of secant lines is mathematically represented as
[tex]\frac{ f(2) - f(1)}{2-1} = \frac{16(2)^3 - 2 - [16(1)^3 -1] }{2-1 } = 113.000[/tex]
For [1, 1.5]
The slopes of secant lines is mathematically represented as
[tex]\frac{ f(1.5) - f(1)}{1.5-1} = \frac{16(1.5)^3 - 1.5 - [16(1)^3 -1] }{1.5-1 } = 75.000[/tex]
For [1, 1.1]
The slopes of secant lines is mathematically represented as
[tex]\frac{ f(1.1) - f(1)}{1.1-1} = \frac{16(1.1)^3 - 1.1 - [16(1)^3 -1] }{1.1-1 } = 51.960[/tex]
For [1, 1.01]
The slopes of secant lines is mathematically represented as
[tex]\frac{ f(1.01) - f(1)}{1.01-1} = \frac{16(1.01)^3 - 1.01 - [16(1)^3 -1] }{1.01-1 } =47.482[/tex]
For [1, 1.001]
The slopes of secant lines is mathematically represented as
[tex]\frac{ f(1.001) - f(1)}{1.001-1} = \frac{16(1.01)^3 - 1.001 - [16(1)^3 -1] }{1.001-1 } =47.048[/tex]
Factor completely 4x^4− 20x^3 + 12x^2
Answer:
Step-by-step explanation:
4x^2(x^2 - 5x + 6)
4x^2(x - 3)(x - 2)
The length of a desk is 3.5 feet. How many centimeters is the length? (There are 2.54 cm in an inch)
Answer:106.
Step-by-step explanation:
HELP ME PLS i truly need help on this
Step-by-step explanation:
75+54
129°
the answer is 129°
у (x) = 5x - 9 find each value
Dhshshsjehsjsjjsjssjsjsjsjsjsjshshdhdhdhdjdjdjdjhdbd djdhdhdjjdjdjdjdjdjd
Answer:
Dhshshshhshsjehsjsjjsjssjsjsjsjsjsjjshhdhddhhdjdjddjdjjhdhdkdhjsdfggdhjjjjd
Step-by-step explanation:
what are the steps to finding a midpoint with decimals?