The term that is the −20,155,392 in the sequence is a₁₀.
What is sequence?A sequence is defined as an arrangement of numbers in a particular order.
The given sequence is 2, -12, 72, -432
a = first term
n = number of terms
r = common ratio
r = -12 / 2 = 72 / -12 = -432 / 72 = -6
a = 2
Therefore, nth term = arⁿ⁻¹
−20,155,392 = 2 × -6ⁿ⁻¹
−20,155,392 / 2 = -6ⁿ⁻¹
- 10077696 = -6ⁿ⁻¹
6ⁿ⁻¹ = 10077696
6ⁿ⁻¹ = 6⁹
n - 1 = 9
n = 9 + 1
n = 10
Hence, it's the 10th term.
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Rachel recorded the number of calls she made at work during the week:
Monday: 18
Tuesday: 14
Wednesday: 24
Thursday: 16
She expected to make 18 calls each day. To answer whether the number of calls follows a uniform distribution, a chi square test for goodness of fit should be performed. (alpha = 0.10)
chi squared equals begin inline style sum from blank to blank of end style fraction numerator left parenthesis O minus E right parenthesis squared over denominator E end fraction
What is the chi squared test statistic? Answers are rounded to the nearest hundredth.
a. 4.61
b. 1.52
c. 3.27
d. 3.11
The value of the chi squared test statistic is 3.27
Chi square test means a statistical test used to compare observed results with expected results.
Here we have given that Rachel recorded the number of calls she made at work during the week:
Monday: 18
Tuesday: 14
Wednesday: 24
Thursday: 16
And we need to find the chi squared test statistic
While looking into the given question, we have identified that, She expected to make 18 calls each day
Here when a test statistic is smaller than in a left tailed test we would reject H₀.
And if we go to the standard normal chart and use 1% or 0.01, we will search for the closest value to 1% as closely as possible.0.0099 corresponds with a z-score of 3.27
Therefore, option (c) is correct.
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Write an equation to show that 68 is 8 times an many as 6.
8x+6=68 is the equation to demonstrate that 68 is 8 times as numerous as 6.
What is meant by an equation?An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable. By deleting parentheses and merging like terms, you can simplify either side of an equation and find its solution.
Identify the variable term on one side of the equation by adding or subtracting. You can find the variable's value by multiplying or dividing. When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. Depending on the language, the definition of the word equation and its cognates may alter slightly. For instance, an equation is what is meant in French.
8x+6=68 is the equation to demonstrate that 68 is 8 times as numerous as 6.
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If 2x-4 = 6, what is the value of 3x + 2?
When 2x-4 = 6, the value of 3x + 2 is 17.
What is the value of 3x + 2?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
When 2x - 4 = 6, the value of x will be:
2x - 4 = 6
2x = 6 + 4
2x = 10
Divide
x = 5
Therefore, 3x + 2 will be:
3x + 2 = 3(5) + 2
= 15 + 2
= 17
The value is 17.
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What are the restrictions on the domain for the following rational expression?
Answer:
x <> -3, 8
Step-by-step explanation:
x² - 5x - 24 (the denominator of the fraction) must not be 0, because n/0 is not defined for any n.
since this is a quadratic equation, it must have 2 solutions.
therefore, the second answer must be right.
let's check.
a quadratic equation
ax² + bx + c = 0
has the solutions
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (5 ± sqrt((-5)² - 4×1×-24))/(2×1) =
= (5 ± sqrt(25 + 96))/2 = (5 ± sqrt(121))/2 =
= (5 ± 11)/2
x1 = (5 + 11)/2 = 16/2 = 8
x2 = (5 - 11)/2 = -6/2 = -3
correct.
If the hours of daylight in Miami can be
approximated using a sinusoidal wave, what is the
amplitude of the function if the shortest day in
Miami is 10 hours and 52 minutes long and the
longest day in Miami is 13 hours and 45 minutes
long?
Answer:
the sinusoidal function that approximates the hours of daylight in Miami has an amplitude of approximately 1.44 hours.
Step-by-step explanation:
The amplitude of a sinusoidal function is half the difference between the maximum and minimum values of the function. In this case, the shortest day in Miami is 10 hours and 52 minutes long, and the longest day is 13 hours and 45 minutes long, so the difference between the maximum and minimum values is 2 hours and 53 minutes, which is equal to 173 minutes. Half of this is 86.5 minutes, which is the amplitude of the function.
To express this in hours, divide the amplitude in minutes by 60. This gives an amplitude of 86.5 / 60 = 1.44 hours.
So, the sinusoidal function that approximates the hours of daylight in Miami has an amplitude of approximately 1.44 hours.
Need an answer please will give Brainliest
The quotient will be = 2m^2 + 6m - 9m
The remainder will be = 0
Long division algorithm is below:
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how to solve 4 divided by 3
Answer:
1.33333 , it just keeps going
Step-by-step explanation:
divide 4/3 you can use a long division or a calculator.
Hope this helps!!
Put the steps up above in order.
Answer:
1. Given
2. Vertical Angles Theorem (1st Occurrence)
3. Vertical Angles Theorem (1st Occurrence)
4. Transitive Property of Congruence
5. Converse of the Alternate Interior Angles Theorem
Step-by-step explanation:
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Transitive Property of Congruence
If one pair of angles is congruent to a third angle, then the first angle is congruent to the third angle.
Converse of the Alternate Interior Angles Theorem
If two lines are intersected by a transversal so that the alternate interior angles are congruent, then the lines are parallel.
[tex]\begin{array}{l|l}\vphantom{\dfrac12} \sf Statements & \sf Reasons \\\cline{1-2}\\1. \; \angle 2 \cong \angle 7 & 1.\; \sf Given\\\\2. \; \angle 2 \cong \angle 3 & 2.\; \sf Vertical\;Angles\;Theorem\;(1st\;Occurrence)\\\\3. \; \angle 6 \cong \angle 7 & 3.\;\sf Vertical\;Angles\;Theorem\;(2nd\;Occurrence)\\\\4. \; \angle 3 \cong \angle 6 & 4.\;\sf Transitive\;Property\;of\;Congruence\\\\5. \; a \parallel b & 5.\;\sf Converse\;of\;the\;Alternate\;Interior\;Angles\;Theorem\\\\ \end{array}[/tex]
From inspection of the given diagram, we can see that angles 2 and 3 are vertical angles, similarly angles 6 and 7 are vertical angles. Therefore, the Vertical Angles Theorem applies.
According to the Transitive Property of Congruence, if ∠2 ≅ ∠7 and ∠2 ≅ ∠3 and ∠6 ≅ ∠7 then ∠3 ≅ ∠6.
The two lines a and b are intersected by transversal [tex]\ell[/tex] so that the alternative interior angles 3 and 6 area congruent, then the lines a and b are parallel. This is the Converse of the Alternate Interior Angles Theorem.
A mammogram is used to screen women for breast cancer. False positives are tests that incorrectly show a positive result. 85% of positive mammograms are actually false positives. If 1,000 women receive mammograms, and 200 are told there is an abnormal finding, how many women are likely to actually have breast cancer?
Answer:
30
Step-by-step explanation:
200 x .15 (1-.85 = .15)
30
2 1/2 + x = 5 1/3
Help is very much appreciated!
20 pts!!
Answer: hope it helps
Step-by-step explanation:
2 1/2 + x = 5 1/3
(2 + 1/2) + x = (5 + 1/3)
6x = 17
x = 17/
6
= 2.83333333
x = 17/
6
≈ 2.833333
[tex] \huge \underline{ \boxed{ \tt Solution: }}[/tex]
[tex] \tt \pink{\large\dagger} \: \: \: \: \: \: 2\dfrac{1}{2} + x = 5\dfrac{1}{3} \\ \tt : \implies \dfrac{5}{2} + x = \dfrac{16}{3} \\ \tt : \implies x = \dfrac{16}{3} - \dfrac{5}{2} \\ \tt : \implies x = \dfrac{16 \times 2}{3 \times 2} - \dfrac{5 \times 3}{2 \times 3} \\ \tt : \implies x = \dfrac{32}{6} - \dfrac{15}{6} \\ \tt : \implies x = \dfrac{32 - 15}{6} \\ \tt : \implies x = \dfrac{17}{6} [/tex]
[tex] \tt \pink{ \star \: Hence \: the \: answer \: is \: \dfrac{17}{6}.}[/tex]
Let f be the continuous function defined on [-4,3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by g(x) = integral^x_1, (t) dt. Find the values of g(2) and g(-2). For each of g'(-3) and g"(-3), find the value or state that it docs not exist. Find the x-coordinate of each point at which the graph of g has a horizontal tangent line. For each of these points, determine whether g has a relative minimum, relative maximum, or neither a minimum nor a maximum at the point. Justify your answers. For -4 < x < 3, find all values of v for which the graph of g has a point of inflection. Explain your reasoning.
a) The value of g(2) = -1/4 and the value of g(-2) = π/2 - 3/2
b) The value of g'(x) = 2 The value of g''(x) =1
c) g has neither a relative maximum nor a relative minimum at x= 1
d) the graph of g has a point of inflection at each of x=-2 , x=0 and x = 1 because g''(x) = f'(x) changes at each of these values.
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
There are several types of functions in maths. Some important types are:
Injective function or One-to-one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
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i need to know the answer to this question
The function type is Linear function.
What is Linear function?
The terms "linear function" in mathematics refer to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
From the given figure it is easily noticed that the function is increasing in nature for [tex]$x < 0$[/tex] and the function is constant in nature for [tex]$x > 0$[/tex] because the value of [tex]$\mathrm{y}$[/tex] remains unchanged for any value of [tex]$\mathrm{x}$[/tex], where [tex]$x \geq 0$[/tex].
The value of function is 3 at x=0.
The value of the function is always 3 for all [tex]$x \geq 0$[/tex]. So, f(x)=3 for [tex]x \geq 0$.[/tex]
The function is a straight line with intercepts (-3,0) and (0,3).
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A cell phone manufacturer guarantees that the mean battery life for its latest cell phone model is at least 36 hours. You are asked to design a hypothesis test to challenge this claim.a. State the null and alternative hypotheses and identify which represents the claim.b. Describe type I and type II errors for a hypothesis test of the claim.c. Explain whether the hypothesis test is left-tailed, right-tailed, or two-tailed.d. Explain how you should interpret a decision that rejects the null hypothesis. e. Explain how you should interpret a decision that fails to reject the null hypothesis.
Null hypothesis: H₀: population mean, μ ≥ 36hours
Alternate hypothesis: H₁: population mean, μ < 36hours
Given that,
A maker of cell phones promises that the average battery life of its most recent cell phone model is at least 36 hours. To refute this assertion, you are required to create a hypothesis test.
We have to find
a. Describe the null and alternative hypotheses, then choose the one that best supports the claim.
b. Explain type I and type II mistakes for the claim's hypothesis test.
c. Describe if the hypothesis test has left-, right-, or two-tailed distributions.
d. Describe how to read a conclusion that rejects the null hypothesis. a. Describe how you should evaluate a choice that does not rule out the null hypothesis.
We know that,
a. Null hypothesis: H₀: population mean, μ ≥36hours
Alternate hypothesis: H₁: population mean, μ < 36hours
b. Type 1 error: is an error made when we reject the null hypothesis, when the null hypothesis is true. This happens the significance level % of time. In our example, a type 1 error would be made when the population mean is actually greater than 36 hours, but we conclude that the population mean is less than 36 hours.
Type 2 error: is an error made when we fail to reject the null hypothesis, when the null hypothesis is false. This is represented by beta. In our example, a type 2 error would be made when the population mean is actually less than 36 hours, but we conclude that the population mean is not less than 36 hours.
c. The test is left tailed since the area of rejection is on the left side (less than side).
d. We would interpret that at x% confidence level (generally 95%), we reject the claim that the population mean is greater than 36 hours. We would conclude that we have enough evidence from the sample that the population mean is significantly less than 36, and hasn't happened as a matter of chance.
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Help please!!!!!! Which table represents a linear equation that has a y-intercept of -3?
Answer: A
Step-by-step explanation:
A y-intercept is a point where a function (i.e a line) intercepts the y-axis.
Every point on the y-axis has a x value of 0.
The ordered pair will look like this (0,y)
In answer a, you have an x value of 0 with a corresponding y value of 3.
This point is (0,3).
You could also graph the points and look for where the function crosses the y-axis.
Use point-slope form to write the equation of a line that passes through the point
(-11, -8) with slope -2/-3
Salaries of 40 college graduates who took a statistics course in college have a mean x of $60.600. Assuming a standard deviation of $13,553 construct a 90% confidence level for estimating the population mean u
The confidence level is 60600<μ<3,524.786, assuming a standard deviation of $13,553 and the confidence level for estimating the population mean is 90%.
What do you mean by confidence level?
A confidence interval is a range of values that can contain the true value of the parameter being studied in statistics. It is created using observed data and calculated at a desired level of confidence.
The confidence level—for instance, a 95% confidence level—relates to the accuracy of the estimation process, not to the degree to which it is certain that the computed confidence interval contains the actual value of the parameter under investigation.
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A water tank initially contained 105 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute How many minutes have passed, m. when the tank contains 181 liters? Round to the nearest hundredth
Answer:
8.44 minutes
Step-by-step explanation:
The tank initially contained 105 liters so the amount of water needed is 181 - 105 = 76 litters
if the rate is 9 L/min then the number of minutes is
76/9 = 8.44 minutes
What’s the solution set of 2x+8>-4x+5
Answer:
x > –1/2
or x > –0.5
Step-by-step explanation:
2x + 8 > – 4x + 5
2x + 4x > 5 – 8
6x > –3
x > –3/6
x > –1/2
or x > –0.5
the following steps are used to set up a : identify your dependent and independent variables plot the data in a 2 dimensional plane. analyze the data to see whether there is a relationship/correlation between the variables. answer
The following steps are used to set up a regression
Regression analysis is a set of statistical methods used for the estimation of relationships between a dependent variable and one or more independent variables. It can be utilized to assess the strength of the relationship between variables and for modeling the future relationship between them.
Here , first we identify which variable is independent and which is affect by this independent variable
Then , we plot the data to analyze the pattern between them
Then we find correlation between them after we will able to draw our conclusion about regression.
Therefore, the regression analyses are performed a couple of times to produce the best analysis results, including the test statistics and the predicted fitted regression.
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What is the exact value of tan 75°?
A.
OB.
O c.
D.
1-
1+
3
1+
1-4
1+√3
1-v3
1+√3
The exact value of the tan(75°), found using trigonometric identities for the tangent of the sum of two angles, indicates that the exact value of tan(75°) is (1+√3/3)/(1 - √3/3))
What are trigonometric identities?Trigonometric identities are equalities of expressions that includes trigonometric functions which are valid for all values of the argument, or the domain of the function.
The exact value of tan(75°) can be found from the formula for the tangent of the sum of two angles as follows;
tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)•tan(B))
tan(75°) = tan(45° + 30°)
tan(45° + 30°) = (tan(45°) + tan(30°))/(1 - tan(45°)•tan(30°))
tan(30°) = √3/3
tan(45°) = 1
tan(45° + 30°) = (1 + √3/3)/(1 - √3/3)
tan(75°) = (1 + √3/3)/(1 - √3/3)
The correct option is therefore option B
[tex]tan(75 ^{ \circ } ) = \dfrac{1 + \frac{ \sqrt{3} }{3} }{1 - \frac{ \sqrt{3} }{3} } [/tex]
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Simplify the expression (-3r^2+13)+2r(r-6)-4r
Answer:
A potential energy function is given by U(x) = (3.6)x + (1.2)x3. What is the force function F(x) that is associated with this potential energy function
Step-by-step explanation:
Write an equation of the line that goes through (-2,7) and (4,7)
Answer:
y=7
Step-by-step explanation:
y is always the same and it is 7
Using Function Notation
State if the following are functions or not.
The following given table with input and output is a function.
What is function?A relation between a domain and range is called a function when each value in the domain only has one value in the range. This notion is violated by relations that are not functions. They have at least one domain value that corresponds to two or more range values.
Write names of type of functions.Into, onto, bijective and surjective are the types of function.
As every input has only one output so the given table is function.
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The following given table with input and output is a function.
What is function?
A function is a self-contained block of code that performs a specific task. It is a logical grouping of instructions and operations that can be used multiple times throughout a program. Functions help to keep code organized and modular, making it easier to debug and maintain. They also allow for code reuse, which can result in faster development times and greater efficiency. Furthermore, functions can be used to pass data between different parts of a program, making it easier to share information and reduce the need for redundant code.
Write names of type of functions.
Into, onto, bijective and surjective are the types of function.
As every input has only one output so the given table is function.
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The store clerk created a display of R rows of cereal boxes. Each row contained 16 boxes. Choose the expression that shows the total number of cereal boxes on display.
Answer:
16R = T or T = 16R
Step-by-step explanation:
R represents the unknown amount of rows and we know there are 16 boxes in each row.
This means to find the total number of boxes on display, you will have to times the number of rows by 16 as the clerk puts 16 boxes of cereal in each row
e.g, if there are 3 rows, then to find the total amount of cereal boxes, you would do 3 × 16 = 48
Since it's an expression, you need something to represent the total number so that can be represented by any letter ( I chose T ) — in most cases you can probably represent the total as x
Hence the expression should be 16R = T or T = 16R
...at least I think so
What is 11.661903 rounded to the nearest hundreth?
Answer:
The number 11.661903 rounded to the nearest hundredth is 11.66.
Step-by-step explanation:
We have the following number:
11.661903And we need to round this number to the nearest hundredth.
To determine that, we can proceed as follows:
1. Round a number to the nearest hundred is equivalent to rounding the number to two decimal places.
2. Now, we can see that the number in the third decimal position or thousandth place is 1:
3. If this number were 5 or greater than 5, we would need to round up that number to the next following number, that is, 7. However, this is not the case.
4. Therefore, if we have to round that number to the nearest hundredth, then the number is 11.66.
Hence, in summary, the number 11.661903 rounded to the nearest hundredth is 11.66.
(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)
Stay positive and Take care,
A fellow mate,
Cheers !
There are a total of 64 students in a drama club and a yearbook club. The drama club has 10 more students than the yearbook club.
Write a system of linear equations that represents this situation. Let x represent the number of students in the drama club and y represent the number of students in the yearbook club.
System of equations:
__x+ __y=64
There are 37 students in drama club and 27 students in yearbook club.
And the system of equations will be 1.x + 1.y = 64.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
Total number of students in drama club and yearbook club = 64,
Also, there is a yearbook club. Students in drama club has 10 more than yearbook club,
If x represents the number of students in the drama club and y represents the number of students in yearbook club.
According to given condition,
x+ y = 64 (1)
and x = y + 10
Substitute the value of x in equation (1),
y + 10 + y = 64
2y = 54
y = 27
And x = 27 + 10 = 37
The required system of equations,
1.x + 1.y = 64
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b. 2/(x-2)(x-3)+2/(x-1)(3-x)+1/(1-x)(2-x)
After using the quadratic equation the answer is [tex]\frac{2\left(x-3\right)}{x-2}+\frac{-x+4}{x-1}[/tex]
What is quadratic equation ?
Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.
Square and quadrangle difficulties have a close relationship with quadratic equations (another name for rectangles). In actuality, the Latin word quadratus, which means square, is the root of the word quadratic.
Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).
[tex]\frac{2}{x-2} (x-3) = \frac{2(x-3)}{x-2} \\\\ \frac{2}{x-1} (3-x) = \frac{2(3-x)}{x-1} \\\\\frac{1}{1-x} (2-x) = \frac{2-x}{1-x} \\\\[/tex]
[tex]\frac{2\left(x-3\right)}{x-2}+\frac{2\left(3-x\right)}{x-1}+\frac{2-x}{1-x}[/tex]
[tex]\frac{2(3-x)}{x-1} + \frac{2-x}{1-x}[/tex]
[tex]\frac{2\left(x-3\right)}{x-2}+\frac{-x+4}{x-1}[/tex]
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what is capacity . please explain
Answer:
Step-by-step explanation:
the ability to hold, receive, store, or accommodate. : a measure of content : the measured ability to contain : volume. a beaker with a capacity of one liter.
Answer:
Capacity is the maximum amount that something can contain; Volume, or the amount that something can produce.
Capacity is a noun
Hope this helps
What is the value of y in the solution to the system of equations?
1/3*+1/4y=1
2x - 3y = -30
-8
-3
8
Answer:
(-3,6)
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] x + [tex]\frac{1}{4}[/tex] y = 1 Divide all the way through by 12 to clear the fraction
4x + 3y = 12 Add this to the second equation
2x -3y = -30
6x = -18 Divide both sides by 6
x = -3
Substitute -3 into either of the original equations to solve for y
4x + 3y = 12
4(-3) + 4y = 12
-12 + 4y = 12 Add 12 to both sides
4y = 24 Divide both sides by 4
y = 6
(b) 2(w 2 5 z)+3(2 x -2 -6)=4(4 7 y 3)
From the given matrices, the values w,x,x and z are 5,-8,4 and -3 respectively.
How to solve matrix equations?Matrices is the rectangular arrangement of numbers and letters in rows and columns
An equation is defined as a mathematical expression showing the equality of two sides of the statement
The given matrices are;
[tex]2\left[\begin{array}{ccc}w&2&\\5&z&\/\end{array}\right] -3\left[\begin{array}{ccc}2&x&\\-2&-6&\\\end{array}\right] =4\left[\begin{array}{ccc}4&7\\y&3\\\end{array}\right][/tex]
Opening the brackets in the matrices
[tex]\left[\begin{array}{ccc}2w&4\\10&2z\\\end{array}\right] -\left[\begin{array}{ccc}6&3x\\-6&-18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y&12\\\end{array}\right][/tex]
Adding the Left hand side
[tex]\left[\begin{array}{ccc}2w-6&4-3x\\16&2x+18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y12&6\\\end{array}\right][/tex]
Equate Left hand side with Right hand side to form linear equations
2w-6=16
2w=10
w=5
4-3x=28
-3x=28-4
-3x=24
x=-8
16=4x
4=x
2z+18=12
2x=12-18
2x=-6
x=-3
These are how the various values are gotten
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