Answer:
-3
Step-by-step explanation:
If these numbers are part of an arithmetic progression, their differences are the same:
(x -7) -(2x +1) = (2x +1) -(x +3)
-x -8 = x -2
-6 = 2x
-3 = x
___
The numbers in the sequence are 0, -5, -10.
Answer:
x = -3.
Step-by-step explanation:
As it is an Arithmetic Progression the differences between successive terms are common, so:
2x + 1 - (x + 3) = x - 7 - (2x + 1)
2x - x + 1 - 3 = x - 2x - 7 - 1
x - 2 = -x - 8
2x = -8 + 2 = -6
x = -3.
it give f(x) = x-3x⁴ +2x³ -4x² +5x -10 and f(4)(x)?
Answer:
f(x) + f(4)
Step-by-step explanation:
TRUST ME DO THIS PROCESS
There are 8 books needing re-shelving in a library where 65% of the library's collection consists of reference books. Let X be the number of reference books a student helper re-shelves out of the 8 on her cart. a) What is the probability that all 8 of them are reference books
Answer:
0.0319
Step-by-step explanation:
To approximate this probability, we shall be using the Bernoulli approximation of the Binomial distribution.
Let p = probability of selecting a reference book = 65% = 0.65
Let q = probability of selecting other books= 1-p = 1-0.65 = 0.35
Now, we want to find the probability that all of these 8 books to be re-shelved are reference book.
We set up the probability as follows;
P(X = 8) = 8C8 •p^8•q^0
P(X = 8) = 1 * (0.65)^8 * (0.35)^0
P(X = 8) = 0.031864481289 which is 0.0319 to 4 decimal places
10. A sample of 60 mutual funds was taken and the mean return in the sample was 13% with a standard deviation of 6.9%. The return on a particular index of stocks (against which the mutual funds are compared) was 11.5%. Therefore, the test statistic is 1.68. When testing the hypothesis that the average return on actively-managed mutual funds is higher than the return on an index of stocks, if the critical value is 1.96, what is your conclusion concerning the null hypothesis
Answer:
In this question, we shall be accepting the null hypothesis H0 since the critical value is greater than the test statistic value
Step-by-step explanation:
Here in this question, we want to make a conclusion about the null hypothesis H0.
To make or give the correct conclusion about the null hypothesis in this case, we shall need to compare the absolute value of the test statistic used against the value of the critical value.
Hence, we draw a conclusion if the test statistic is larger or smaller than the critical value.
From the value given in the question, we can see that the test statistic given as 1.68 is lesser in value compared to the critical value given as 1.96.
In this kind of case, the conclusion that we shall be drawing is that we will accept the null hypothesis H0 and reject the alternative hypothesis
Solve for x: −3|x + 7| = −12
x = 5 over 3, x = −19 over 3
x = −3, x = −11
x = −3, x = 11
No solution
Answer:
x=-3 x=-11
Step-by-step explanation:
−3|x + 7| = −12
|x + 7|=4
x+7=4 x+7=-4
x=-3 x=-11
Question 2 Select the correct statement(s) about the Model Evaluation stage of the data science methodology.
Answer:
where is the whole question
Sociologists say that 90% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that seven married women are having coffee together one morning. Find the following probabilities. (For each answer, enter a number. Round your answers to three decimal places.) (a) All of them dislike their mother-in-law. (b) None of them dislike their mother-in-law. (c) At least five of them dislike their mother-in-law. (d) No more than four of them dislike their mother-in-law.
For each married women, there are only two possible outcomes. Either they dislike their mother in law, or they do not. The probability of a women disliking their mother in law is independent of any other women, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
90% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention).
This means that [tex]p = 0.9[/tex]
Suppose that seven married women are having coffee together one morning.
This means that [tex]n = 7[/tex]
Question a:
This is P(X = 7), so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{7,7}.(0.9)^{7}.(0.1)^{0} = 0.4783[/tex]
Thus, 0.4783 = 47.83% probability that all of them dislike their mother-in-law.
Question b:
This is P(X = 0), so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{7,0}.(0.9)^{0}.(0.1)^{7} = 10^{-7}[/tex]
Thus, [tex]10^{-7}[/tex] probability that none of them dislike their mother-in-law.
Question c:
This is:
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7)[/tex], so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{7,5}.(0.9)^{5}.(0.1)^{2} = 0.1240[/tex]
[tex]P(X = 6) = C_{7,6}.(0.9)^{6}.(0.1)^{1} = 0.3720[/tex]
[tex]P(X = 7) = C_{7,7}.(0.9)^{7}.(0.1)^{0} = 0.4783[/tex]
Then
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) = 0.1240 + 0.3720 + 0.4783 = 0.9743[/tex]
0.9743 = 97.43% probability that at least five of them dislike their mother-in-law.
Question d:
This is:
[tex]P(X \leq 4) = 1 - P(X > 4)[/tex]
Considering [tex]P(X > 4) = P(X \geq 5) = 0.9743[/tex]:
[tex]P(X \leq 4) = 1 - P(X > 4) = 1 - 0.9743 = 0.0257[/tex]
Thus, 0.0257 = 2.57% probability that no more than four of them dislike their mother-in-law.
For another example of the binomial distribution, you can check https://brainly.com/question/15557838
which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 9xy³ -4y⁴ -10x²y² + x³y + 3x⁴ + 2x²y² - 9y⁴
Answer:
3x^4+(x^3)y-8x^2y^2+9xy^3-13y^4
Step-by-step explanation:
3x^4+(nothing)=3x^4
x^3y+(nothing)=x^3y
-10x^2y^2=2x^2y^2=-8x^2y^2
9xy^3+(nothing)=0
-4y^4-9y^4=-13y^4
Add it all up and write the terms by descending order of exponent value, and u get my answer.
A store is advertising a new DVD player for $189.00. If the sales tax rate is 7.25 percent,
Answer:
then what's the question???..
Find a • b. a = 5i + 7j, b = -4i + 3j 1 41
Answer:
[tex]\boxed{-20i^2 -13ij+21j^2}[/tex]
Step-by-step explanation:
[tex]\sf Plug \ in \ the \ values.[/tex]
[tex](5i+7j) \cdot (-4i+3j)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]5i(-4i+3j)+7j(-4i+3j)[/tex]
[tex]-20i^2 +15ij+-28ij +21j^2[/tex]
[tex]\sf Combine \ like \ terms.[/tex]
[tex]-20i^2 -13ij+21j^2[/tex]
Triangle DEF has sides of length x, x+3, and x−1. What are all the possible types of DEF?
Triangle DEF is scalene
Must click thanks and mark brainliest
The triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
What is a scalene triangle?A scalene triangle is a type of triangle which have all the sides to be unequal and similarly, all the angles will also be unequal to each other.
Given that:-
Triangle DEF has sides of length x, x+3, and x−1it is given that all the sides of the triangle are x, x+3, and x−1 we can clearly see that for any value of x all the three sides will have different values. we can conclude from this that the triangle DEF is a scalene triangle.
Therefore triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
To know more about the scalene triangle follow
https://brainly.com/question/16589630
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Find the value of x , 5x =625 , also find 3x and 2x-1
Answer:
That's your answer
x= 125
3x= 375
2x-1= 249
You are studying for your final exam of the semester up to this point you received 3 exam scores of 61% 62% and 86% to receive a grade of c and the class you must have an average exam score between 70% and 79% for all four exams including the final find the widest range of scores that you can get on the final exam in order to receive a grade of C for the class 63 to 100% 71 to 100% 68 to 97
There will be a total of 4 test scores including the final exam. To get a 70, the 4 tests need to equal 4 x 70 = 280 points , to be 79, they have to equal 4 x 79 = 316 points.
The 3 already done = 61 + 62 + 86 = 209 points.
The final exam needs to be between :
280 -209 = 71
316 -209 = 107. The answer would be between 71 and 100%
If cot Theta = Two-thirds, what is the value of csc Theta? StartFraction StartRoot 13 EndRoot Over 3 EndFraction Three-halves StartFraction StartRoot 13 EndRoot Over 2 EndFraction Eleven-thirds
Answer:
csctheta= [tex]\frac{\sqrt{13} }{3}[/tex]
Step-by-step explanation:
answer is provided on top
The value of the [tex]\rm cosec \theta = \frac{\sqrt{13} }{3}[/tex]. Cosec is found as the ratio of the hypotenuse and the perpendicular.
What is trigonometry?The field of mathematics is concerned with the relationships between triangles' sides and angles, as well as the related functions of any angle
The given data in the problem is;
[tex]\rm cot \theta = \frac{2}{3}[/tex]
The [tex]cot \theta[/tex] is found as;
[tex]\rm cot \theta = \frac{B}{P} \\\\ \rm cot \theta = \frac{2}{3} \\\\ B=2 \\\\ P=3 \\\\[/tex]
From the phythogorous theorem;
[tex]\rm H=\sqrt{P^2+B^2} \\\\ \rm H=\sqrt{2^2+3^2} \\\\ H=\sqrt{13} \\\\[/tex]
The value of the cosec is found as;
[tex]\rm cosec \theta = \frac{H}{P} \\\ \rm cosec \theta = \frac{\sqrt{13} }{3}[/tex]
Hence the value of the [tex]\rm cosec \theta = \frac{\sqrt{13} }{3}[/tex].
To learn more about the trigonometry refer to the link;
https://brainly.com/question/26719838
m+1/4d=7 solve for d
Answer:
d = -4M + 28
Step-by-step explanation:
A Circuit has a 5000 V power supply(AC), A load resistance of 4 ohms and open switch how much Current will flow in a circuit as it is ?
Answer:
1250 amps
Step-by-step explanation:
V = 5000 V
R = 4 ohms
Use ohms law: V = IR
5000 =I(4)
I = 1250 amps
State the correct polar coordinate for the graph shown.
It is not the option selected.
One way to write this polar coordinate is to say (2.5, pi/2) meaning we move 2.5 units away from the origin toward the pi/2 direction
pi/2 radians = 90 degrees
An alternative is to write (-2.5, 3pi/2) which is where we aim at the 3pi/2 direction (270 degrees) and walk backward while still facing directly south, and we'll arrive at the same location.
Find the work W done by a force of 7pounds acting in the direction 30 degreesto the horizontal in moving an object 7feet from (0 comma 0 )to (7 comma 0 ).
Answer:
The work done by the force is 42.4 Joules
Step-by-step explanation:
The force F = 7 pounds
angle to the horizontal that the force acts ∅ = 30°
The object is moved a distance d = 7 feet
The coordinate (0 comma 0 )to (7 comma 0 ), indicates that the movement started from the origin, and is along the x-axis.
The work done by this force = F cos ∅ x d
==> 7 cos 30° x 7
==> 7 x 0.866 x 7 = 42.4 Joules
What is the solution to 5x - 15 = 5(-4x - 3) ? Group of answer choices -12 6 0 -16
Answer:
x = 0Step-by-step explanation:
5x - 15 = 5(-4x - 3)
Multiply the terms in the bracket
5x - 15 = - 20x - 15
Group like terms
Send the constants to the right side of the line and those with variables to the left side
That's
5x + 20x = - 15 + 15
Simplify
25x = 0
Divide both sides by 25
We have the final answer as
x = 0Hope this helps you
Answer:
x=0
Step-by-step explanation:
5x - 15 = 5(-4x - 3)
To find the solution to this equation, we have to get x by itself on one side of the equation.
First, distribute the 5 on the right side. Multiply each term by 5.
5x - 15= (5*-4x) + (5*-3)
5x-15 = -20x + (5*-3)
5x-15= -20x -15
Next, add 20x to both sides of the equation.
(5x+20x) -15 = (-20x+20x) -15
(5+20x) -15 = -15
25x -15=-15
Next, add 15 to both sides of the equation.
25x -15 +15 = -15+15
25x= -15+15
25x=0
Finally, divide both sides of the equation by 25.
25x/25=0/25
x= 0/25
x= 0
The solution to this equation is x=0
Sketch the graph of the following equations:
y-3x+5
y=-3x-5
A test-preparation company advertises that its training program raises SAT scores by an average of at least 30 points. A random sample of test-takers who had completed the training showed a mean increase smaller than 30 points.
(a) Write the hypotheses for a left-tailed test of the mean.
(b) Explain the consequences of a Type I error in this context.
Answer:
(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 30 points
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 30 points
(b) Type I error is that we conclude that test-takers who had completed the training showed a mean increase smaller than 30 points but in actual, the program raises SAT scores by an average of at least 30 points.
Step-by-step explanation:
We are given that a test-preparation company advertises that its training program raises SAT scores by an average of at least 30 points.
A random sample of test-takers who had completed the training showed a mean increase smaller than 30 points.
Let [tex]\mu[/tex] = average SAT score.
(a) So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 30 points
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 30 points
Here, the null hypothesis states that the training program raises SAT scores by an average of at least 30 points.
On the other hand, the alternate hypothesis states that test-takers who had completed the training showed a mean increase smaller than 30 points.
(b) Type I error states the probability of rejecting the null hypothesis given the fact that null hypothesis is true.
According to the question, the Type I error is that we conclude that test-takers who had completed the training showed a mean increase smaller than 30 points but in actual, the program raises SAT scores by an average of at least 30 points.
The consequence of a Type I error is that we conclude the test-takers have low SAT scores but in actual they have an SAT score of at least 30 points.
Lavania is studying the growth of a population of fruit flies in her laboratory. After 6 days she had nine more than five times as many fruit flies as when she began the study. If she observes 20 fruit flies on the first day of the study, write and evaluate an expression to find the population of fruit flies Lavania observed after 6 days
a. write an expression for the population of fruit flies Lavania observed after 6 days
b. find the population of fruit flies Lavania observed after 6 days
Answer:
A. 20•5+9
B.109 flies
Solve for x: the quantity of x plus 4 over 3 = 2.
Answer:
x =2
Step-by-step explanation:
(x+4) /3 = 2
Multiply each side by 3
(x+4) /3 *3= 2*3
x+4 = 6
Subtract 4
x+4-4 = 6-4
x =2
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 2
▹ Step-by-Step Explanation
[tex]\frac{x + 4}{3} = 2\\\\3 * 2 = 6\\\\x + 4 = 6\\\\x = 2[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
The local bowling alley pays you
$7.25 per hour to manage the desk.
Last week you worked 16 hours.
What is your straight-time pay?
Answer:
my straight time payment will be $116 for last week
Step-by-step explanation:
The local bowling alley pays
$7.25 per hour to manage the desk.
If worked 16 hours, my straight time payment will be
Rate= $7.25 per hour
Hour worked= 16 hours
my straight time payment = rate*hour worked
my straight time payment = 7.25*16
my straight time payment = 166.00
my straight time payment will be $116
4) Daily tickets to Six Flags cost $50 each.
Variable #1:
What is the variable
Answer:
Amount of tickets
Step-by-step explanation:
The variable is the amount of tickets purchased because that is the only thing that changes, according to the statement that says that daily tickets are $50.
Using the identity (a + b) (a - b) = a - b², evaluate 49 × 51.
[tex]\\ \sf\longmapsto 49\times 51[/tex]
[tex]\\ \sf\longmapsto (50-1)(50+1)[/tex]
[tex]\\ \sf\longmapsto (50)^2-(1)^2[/tex]
[tex]\\ \sf\longmapsto 2500-1[/tex]
[tex]\\ \sf\longmapsto 2499[/tex]
49 × 51
Using Identity(a + b) (a - b) = a - b²Solution⇛(50 + 1) (50 - 1)
⇛(50)² - (1)²
⇛2500 - 1
⇛2499
What is 6 divided by 3/8?
Answer:
16Step-by-step explanation:
[tex]6 \div \frac{3}{8} = 6 \times \frac{8}{3} \\ [/tex]
[tex] = \frac{6 \times 8}{3} \\ \\ = \frac{48}{3} =1 6[/tex]
What are the solutions to the system of equations? {y=2x2−8x+5y=x−2 (3.5, 0.5) and (1, −1) (7, 5) and (0.5, −1.5) (3.5, 1.5) and (1, −1) (3.5, 1.5) and (−1, −3)
Answer:
[tex](1,-1)[/tex] and [tex](3.5,1.5)[/tex]
Step-by-step explanation:
Given
[tex]y = 2x^2 - 8x+5[/tex]
[tex]y = x - 2[/tex]
Required
Determine the solution
Substitute x - 2 for y in [tex]y = 2x^2 - 8x+5[/tex]
[tex]x - 2 = 2x^2 - 8x+5[/tex]
Collect like terms
[tex]0 = 2x^2 - 8x - x + 5 + 2[/tex]
[tex]0 = 2x^2 - 9x + 7[/tex]
Expand the expression
[tex]0 = 2x^2 - 7x - 2x+ 7[/tex]
Factorize
[tex]0 = x(2x - 7) -1(2x - 7)[/tex]
[tex]0 = (x-1)(2x - 7)[/tex]
Split the expression
[tex]x - 1 = 0[/tex] or [tex]2x - 7 = 0[/tex]
Solve for x in both cases
[tex]x = 1[/tex] or [tex]2x = 7[/tex]
[tex]x = 1[/tex] or [tex]2x/2 = 7/2[/tex]
[tex]x = 1[/tex] or [tex]x = 3.5[/tex]
Recall that
[tex]y = x - 2[/tex]
When [tex]x = 1[/tex]
[tex]y = 1 -2[/tex]
[tex]y = -1[/tex]
When [tex]x = 3.5[/tex]
[tex]y = 3.5 - 2[/tex]
[tex]y = 1.5[/tex]
Hence, the solution is;
[tex](1,-1)[/tex] and [tex](3.5,1.5)[/tex]
The areas of two similar octagons are 4 m² and 9 m². What is the scale factor of their side lengths? PLZ PLZ HELP PLZ
Answer:
[tex] \frac{2}{3} [/tex]
Step-by-step explanation:
Area of Octagon A = 4 m²
Side length of Octagon A = a
Area of Octagon B = 9 m²
Side length of Octagon B = b
The scale factor of their side lengths = [tex] \frac{a}{b} [/tex]
According to the area of similar polygons theorem, [tex] \frac{4}{9} = (\frac{a}{b})^2 [/tex]
Thus,
[tex] \sqrt{\frac{4}{9}} = \frac{a}{b} [/tex]
[tex] \frac{\sqrt{4}}{\sqrt{9}} = \frac{a}{b} [/tex]
[tex] \frac{2}{3} = \frac{a}{b} [/tex]
Scale factor of their sides = [tex] \frac{2}{3} [/tex]
Answer:
3:5
Step-by-step explanation:
square root of 9 is 3.
square root if 25 is 5.
therefore, 3:5.
Find a formula for the given polynomial.
In this question, we have to identify the zeros of the polynomial, along with a point, and then we get that the formula for the polynomial is:
[tex]p(x) = -0.5(x^3 - x^2 + 6x)[/tex]
------------------------
Equation of a polynomial, according to it's zeros:
Given a polynomial f(x), this polynomial has roots such that it can be written as: , in which a is the leading coefficient.
------------------------
Identifying the zeros:
Given the graph, the zeros are the points where the graph crosses the x-axis. In this question, they are:
[tex]x_1 = -2, x_2 = 0, x_3 = 3[/tex]
Thus
[tex]p(x) = a(x - x_{1})(x - x_{2})(x-x_3)[/tex]
[tex]p(x) = a(x - (-2))(x - 0)(x-3)[/tex]
[tex]p(x) = ax(x+2)(x-3)[/tex]
[tex]p(x) = ax(x^2 - x + 6)[/tex]
[tex]p(x) = a(x^3 - x^2 + 6x)[/tex]
------------------------
Leading coefficient:
Passes through point (2,-8), that is, when [tex]x = 2, y = -8[/tex], which is used to find a. So
[tex]p(x) = a(x^3 - x^2 + 6x)[/tex]
[tex]-8 = a(2^3 - 2^2 + 6*2)[/tex]
[tex]16a = -8[/tex]
[tex]a = -\frac{8}{16} = -0.5[/tex]
------------------------
Considering the zeros and the leading coefficient, the formula is:
[tex]p(x) = -0.5(x^3 - x^2 + 6x)[/tex]
A similar problem is found at https://brainly.com/question/16078990
The formula that represents the polynomial in the figure is [tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex].
Based on the Fundamental Theorem of Algebra, we understand that Polynomials with real Coefficient have at least one real Root and at most a number of Roots equal to its Grade. The Grade is the maximum exponent that Polynomial has and root is a point such that [tex]p(x) = 0[/tex]. By Algebra we understand that polynomial can be represented in this manner known as Factorized form:
[tex]p(x) = \Pi\limits_{i=0}^{n} (x-r_i)[/tex] (1)
Where:
[tex]n[/tex] - Grade of the polynomial.
[tex]i[/tex] - Index of the root binomial.
[tex]x[/tex] - Independent variable.
We notice that polynomials has three roots in [tex]x = -2[/tex], [tex]x = 0[/tex] and [tex]x = 3[/tex], having the following construction:
[tex]p(x) =(x+2)\cdot x \cdot (x-3)[/tex]
[tex]p(x) = (x^{2}+2\cdot x)\cdot (x-3)[/tex]
[tex]p(x) = x^{3}+2\cdot x^{2}-3\cdot x^{2}-6\cdot x[/tex]
[tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex]
The formula that represents the polynomial in the figure is [tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex].
Here is a question related to the determination polynomials: https://brainly.com/question/10241002
WILL GIVE BRAINLYEST AND 30 POINTS Which of the followeing can be qritten as a fraction of integers? CHECK ALL THAT APPLY 25, square root of 14, -1.25, square root 16, pi, 0.6
Answer:
25 CAN be written as a fraction.
=> 250/10 = 25
Square root of 14 is 3.74165738677
It is NOT POSSIBLE TO WRITE THIS FULL NUMBER AS A FRACTION, but if we simplify the decimal like: 3.74, THEN WE CAN WRITE THIS AS A FRACTION
=> 374/100
-1.25 CAN be written as a fraction.
=> -5/4 = -1.25
Square root of 16 CAN also be written as a fraction.
=> sqr root of 16 = 4.
4 can be written as a fraction.
=> 4 = 8/2
Pi = 3.14.........
It is NOT POSSIBLE TO WRITE THE FULL 'PI' AS A FRACTION, but if we simplify 'pi' to just 3.14, THEN WE CAN WRITE IT AS A FRACTION
=> 314/100
.6 CAN be written as a fraction.
=> 6/10 = .6