the sum between negative 4 and 13, this can be tought as:
Stepping on -4 and moving 13 units to the right.Stepping on 13 and moving 4 units to the left.Which is the interpretation of the given expression?
The expression is just the sum:
-4 + 13
So we have the sum between negative 4 and 13, this can be tought as:
Stepping on -4 and moving 13 units to the right.Stepping on 13 and moving 4 units to the left.Now, none of the written options (a, b, and c) depict any of this, so I assume that the correct option is the one that you did not write, which is option D.
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Show that the curve x = 7 cos(t), y = 4 sin(t) cos(t) has two tangents at (0, 0) and find their equations
The equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and
[tex]y = -\frac{4}{7} x[/tex].
In this question,
The curves are x = 7 cos(t), y = 4 sin(t) cos(t)
Two tangents at (0, 0)
In this case, the parametric derivative of x and y are expressed in terms of t.
The first derivative dy/dx can be expressed as
[tex]\frac{dy}{dx}=\frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
Now, dy/dt is obtained by differentiate y with respect to t,
[tex]\frac{dy}{dt}= 4[cos(t)(cos(t))+sin(t)(-sin(t))][/tex]
⇒ [tex]\frac{dy}{dt}= 4[cos^{2} (t)-sin^{2} (t)][/tex]
Now, dx/dt is obtained by differentiate x with respect to t,
[tex]\frac{dx}{dt} =7(-sin(t))[/tex]
⇒ [tex]\frac{dx}{dt} =-7sin(t)[/tex]
Thus, [tex]\frac{dy}{dx}=\frac{4[cos^{2}(t)-sin^{2}(t ) ]}{-7sin(t)}[/tex]
At (0,0) x = 0 and y = 0, Then
0 = 7 cos(t)
0 = 4 sin(t) cos(t)
and
cos(t) = 0
sin(t) cos(t) = 0
There are two values between -π and π which satisfy these equations simultaneously are
t = π/2
t = -π/2
The equation of a straight line given a point and its slope is
y-y₀ = m(x-x₀)
The two tangents lies at (0,0), so the equation becomes
y = mx
Then the two straight lines will be
y = m₁x and
y = m₂x
For t = π/2,
[tex]m_1=\frac{dy}{dx}=\frac{4[cos^{2}(\frac{\pi }{2} )-sin^{2}(\frac{\pi }{2} ) ]}{-7sin(\frac{\pi }{2} )}[/tex]
⇒ [tex]m_1=-\frac{4[0-1]}{7(1)}[/tex]
⇒ [tex]m_1=\frac{4}{7}[/tex]
For t = -π/2,
[tex]m_2=\frac{dy}{dx}=\frac{4[cos^{2}(-\frac{\pi }{2} )-sin^{2}(-\frac{\pi }{2} ) ]}{-7sin(-\frac{\pi }{2} )}[/tex]
⇒ [tex]m_2=-\frac{4[0-1]}{-7(1)}[/tex]
⇒ [tex]m_2=-\frac{4}{7}[/tex]
Thus the equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and
[tex]y = -\frac{4}{7} x[/tex].
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Complete the ratio table to convert the units of measure from ounces to grams or grams to ounces.
Ounces Grams
111 282828
333
140140140
The ratio illustrates that the values will be 3146.7945 gram, 9440.3835 gram, and 3968.93 grams.
How to illustrate the information?It should be noted that 1 ounce is equivalent to 28.3495 gram.
Therefore, 111 ounces will be:
= 111 × 28.3495 gram
= 3146.7945 gram
333 ounces will be:
= 333 × 28.3495 gram
= 9440.3835 gram
140 ounces will be:
= 140 × 28.3495 gram
= 3968.93 grams
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Choose the system for the graph.
y 2 2x+2
y2-x
A.
B.
C.
D.
≤ 2x - 1
yz -x + 2
y≤-2x + 2
(y 2 x
ys 2x + 2
y >- 1x
Answer:
[tex]\textsf{D.} \quad \begin{cases} y \leq 2x+2 \\ y\geq -\dfrac{1}{2}x \end{cases}[/tex]
Step-by-step explanation:
Both lines in the given system of inequalities are linear equations.
Slope-intercept form of a linear equation: y = mx + b
(where m is the slope and b is the y-intercept)
Positive slope (m): as x increases, y increases.
Negative slope (-m): as x increases, y decreases.
When graphing inequalities:
< or > : dashed lines≤ or ≥ : solid line< or ≤ : shading under the line> or ≥ : shading above the lineThe inequality represented by the blue line has a positive slope and shading below the line.
⇒ y ≤ mx + b
From inspection of the graph, its y-intercept is 2.
⇒ y ≤ mx + 2
The inequality represented by the yellow line has a negative slope and shading above the line.
⇒ y ≥ -mx + b
From inspection of the graph, it's y-intercept is zero.
⇒ y ≥ -mx
The only pair of inequalities that satisfies the above conditions is:
[tex]\textsf{D.} \quad \begin{cases} y \leq 2x+2 \\ y\geq -\dfrac{1}{2}x \end{cases}[/tex]
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Factor the polynomial expression 3x² + 2.
A. (√3x + √2i)(√3x - √/2i)
B. (3x + √2i)(3x - √2i)
C. (√3x + √2)(√3x - √2)
D. (√3x + i)(√√3x - i)
Answer:
[tex]\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}[/tex]
Step-by-step explanation:
Setting the expression equal to zero to find the roots,
[tex]3x^2 +2=0\\\\3x^2 =-2\\\\x^2 =-\frac{2}{3}\\\\x=\pm i\sqrt{\frac{2}{3}}[/tex]
This means that
[tex]3x^2 +2=\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}[/tex]
A recipe requires 3.5 teaspoons of sugar to make a tart. which equation shows the number of teaspoons of sugar, y, needed to make x tarts? x = 3.5y y = 3.5x y = 3.5 x x = 3.5 y
x = 3.5y equation shows the number of teaspoons of sugar, y, needed to make x tarts.
What is the linear equation in two variable?
Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called linear equation in two variable.
According to the given question
A recipe require 3.5 teaspoons of sugar to make a tart.
y represents the number of teaspoons of sugar.
x represents the number of tarts.
Now, for x tart 3.5y teaspoons of sugar required.
⇒ x = 3.5y
Hence, the linear equation in two variable that shows the number of teaspoons of sugar y, needed to make x number or tarts is x = 3.5y.
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A test consists of section A and section B. Section A has 15 questions and section B has 10 questions. The number of questions in section A is ____% if the questions in the test.
Evaluate the following integral (Calculus 2) Please provide step by step explanation!
Answer:
[tex]\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=-\dfrac{2}{x+1}+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given integral:
[tex]\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x[/tex]
Factor the denominator:
[tex]\begin{aligned}\implies x^2+2x+1 & = x^2+x+x+1\\& = x(x+1)+1(x+1)\\& = (x+1)(x+1)\\& = (x+1)^2\end{aligned}[/tex]
[tex]\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int \dfrac{2}{(x+1)^2}\:\:\text{d}x[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]
[tex]\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int 2(x+1)^{-2}\:\:\text{d}x[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $ax^n$}\\\\$\displaystyle \int ax^n\:\text{d}x=\dfrac{ax^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
Use Integration by Substitution:
[tex]\textsf{Let }u=(x+1) \implies \dfrac{\text{d}u}{\text{d}x}=1 \implies \text{d}x=\text{d}u}[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x & = \int 2(x+1)^{-2}\:\:\text{d}x\\\\& = \int 2u^{-2}\:\:\text{d}u\\\\& = \dfrac{2}{-1}u^{-2+1}+\text{C}\\\\& = -2u^{-1}+\text{C}\\\\& = -\dfrac{2}{u}+\text{C}\\\\& = -\dfrac{2}{x+1}+\text{C}\end{aligned}[/tex]
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Select the correct answer.
Based on the construction shown, what is the next step in the process of constructing parallel line CD?
A.
Using the same compass width that created the first arc, repeat the arc centered at point B.
B.
Using the same compass width that created the first arc, repeat the arc centered at point C.
C. Set the compass width to the distance between point E and where the arc crosses line AB.
D.Set the compass width to be where the arc intersects lines ECand EB.
The next step in the process of constructing parallel line CD is C. Set the compass width to the distance between point E and where the arc crosses line AB.
How to illustrate the information?It's important to draw a line parellel to line AB. Then, on should set compasses' width to the distance where the lower arc crosses the two lines.
After that, it's vital to move the compasses to where the upper arc crosses the transverse.
In conclusion, the correct option is C.
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Answer:
The answer is A
Step-by-step explanation:
Select all the correct answers. a group of scientists is conducting an experiment on the effects of media on children. they randomly select 100 children and randomly assign each child to one of four treatment groups. each treatment group has a specific amount of screen time during a one-week time frame. the first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth group has six hours of screen time. after the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group experiences each of the four treatments. which statements about this study are true?
Answer:
This study uses random sampling
This study uses a control group
This study uses a repeated measures design
Answer:
this study uses random sampling
this study uses a control group
this study uses a repeated measures design
Step-by-step explanation:
plato 2022
With another study, where you also plan on evaluating a mean using the t statistic, you have a sample of n = 21 that has an ss of 500. what is the variance for the sample? 22. 36 250,000 25 5. 0
The variance for the sample is 25
For given question,
We have been given the sample size n = 21
and the sum of squares is SS = 500
We need to find the variance for the sample.
We know that the variance is mathematically represented as,
[tex]\sigma^2=\frac{SS}{n-1}[/tex]
Substituting given values in the above formula,
[tex]\Rightarrow \sigma^2\\\\=\frac{500}{21-1}[/tex]
= 500 / 20
= 25
So, the variance is 25
Therefore, the variance for the sample is 25
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The water usage at a car wash is modeled by the equation w(x) = 5x3 9x2 − 14x 9, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day. c(x) = 5x3 7x2 − 14x − 6 c(x) = 4x3 7x2 − 14x 6 c(x) = 4x3 7x2 − 14x − 6 c(x) = 5x3 7x2 − 14x 6
The function to model the water used by the car wash on a shorter day is (C) [tex]4x^{3} +7x^{2} -14x-6[/tex].
What is a function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).To find the function to model the water used by the car wash on a shorter day:
Given that the amount of water used on normal days is given by the equation:
[tex]W(x) =5x^{3} +9x^{2} -14x+9[/tex] ......(1)The amount of decrease in water used is modeled by the equation:
[tex]D(x)=x^{3} +2x^{2} +15[/tex] ......(2)To get the function [tex]C(x)[/tex] that models the water used by the car wash on a shorter day you subtract equation (2) from equation (1).
[tex]5x^{3} +9x^{2} -14x+9-(x^{3} +2x^{2} +15)\\5x^{3} +9x^{2} -14x+9-x^{3} -2x^{2} -15\\4x^{3} +7x^{2} -14x-6[/tex]Therefore, the function to model the water used by the car wash on a shorter day is (C) [tex]4x^{3} +7x^{2} -14x-6[/tex].
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The correct question is shown below:
The water usage at a car wash is modeled by the equation w(x) = 5x3 9x2 − 14x 9, where w is the amount of water in cubic feet and x is the number of hours the car wash is open. the owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. the amount of decrease in water used is modeled by d(x) = x3 2x2 15, where d is the amount of water in cubic feet and x is time in hours. write a function, c(x), to model the water used by the car wash on a shorter day.
(A) c(x) = 5x3 7x2 − 14x − 6
(B) c(x) = 4x3 7x2 − 14x 6
(C) c(x) = 4x3 7x2 − 14x − 6
(D) c(x) = 5x3 7x2 − 14x 6
The price of a bus ticket to Saskatoon is $180. This bus has 56 seats. The bus company is considering dropping the bus fare as part of a promotion to increase the ridership on that route. Lately, the busses have only been at half capapcity. The bus company's research shows that for every $5 decrease they will gain 2 more riders.
a) define variables and set up an equation to represent this scenario
b) What is the maximum revenue the bus company can earn and what will be the cost of a ticket when the revenue is at a maximum
If the price of one ticket of bus is $180 and the bus has 56 seats then the maximum revenue that it can earn is $5107.6
Given that the price of a bus ticket to Saskatoon is $180 and the bus has 56 seats.
We are required to find the maximum revenue that the bus company can earn.
Suppose x represents the number of seats, y represents the total amount.
Price=$156
Seats=56
When the bus is of half capacity the bus seats will be 28.
As price decreases th rider gains 2 more.
Revenue equation.
y=(156.5x)(28+2x)-------------1
Expanding the equation.
y=4368-140x+312-10[tex]x^{2}[/tex]
Differentiating with respect to x.
dy/dx=0-140+312-20x
=172-20x
Put dy/dx=0
172-20x=0
x=8.6
Substitute the value of variable x in the equation 1.
y=(156-5x)(28+2x)
=$5107.6
Hence the maximum revenue that the bus company can earn is $5107.6.
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A sample is selected from a population with a mean of μ = 65 and a standard deviation of σ = 15. if the sample has n = 9 scores, what are the expected value of m and the standard error of m?
The Expected value of M is 65
The Standard error of M is 5
The mean of the distribution of sample means is called the expected value of M.The standard deviation of the distribution of sample means is called the standard error of M.Given,
The sample score, n = 9
The Standard deviation, σ = 15
Population mean, μ = 65
Then,
The Expected value of M = μ
∴ The Expected value of M = 65
The Standard error of M = σ/[tex]\sqrt{n}[/tex]
[tex]=\frac{15}{\sqrt{9} } \\\\=\frac{15}{3} \\=5[/tex]
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A casino offers the following game: you draw one card from a standard 52-card deck. If you draw a jack, you win $1.25. If you draw a queen, you win $3.25. If you draw a king, you win $4.5 dollars. If you draw any ace except the ace of spades, you win $6.5. If you draw the ace of spades, you win $7.75. The entry fee to play this game is $1.75. Compute the expected value of this gamble (include the entry fee in your expected value).
Let [tex]W[/tex] be the random variable for the winnings from playing the game once.
• There are 4 jacks in the deck, so you draw a jack with probability 4/52 = 1/13. In this case you "win" $1.25 - $1.75 = -$0.50.
• There are 4 queens, with draw probability 4/52 = 1/13 and winnings $3.25 - $1.75 = $1.50.
• There are 4 kings, with draw probability 4/52 = 1/13 and winnings $4.50 - $1.75 = $2.75.
• There are 4 aces, and 3 of these are not of the spade suit, so the probability of drawing any of these is 3/52 and you win $6.50 - $1.75 = $4.75.
• There is only 1 ace of spaces, with draw probability 1/52 and winnings $7.75 - $1.75 = $6.00.
• Adding these up, it follows that the probability of drawing any other card is 1 - (1/13 + 1/13 + 3/52 + 1/52) = 10/13, in which you have the privilege of "winning" -$1.75.
So, the probability mass function for [tex]W[/tex] is
[tex]\mathrm{Pr}(W=w) = \begin{cases} \dfrac1{13} & \text{if } w \in \{-\$0.50, \$1.50, \$2.75\} \\\\ \dfrac3{52} & \text{if } w = \$4.75 \\\\ \dfrac1{52} & \text{if } w = \$6.00 \\\\ \dfrac{10}{13} & \text{if } w = -\$1.75 \\\\ 0 & \text{otherwise} \end{cases}[/tex]
The expected winnings from playing one round of this game are
[tex]\Bbb E[W] = \displaystyle \sum_w w\,\mathrm{Pr}(W=w)[/tex]
[tex]\Bbb E[W] = \dfrac{-\$0.50 + \$1.50 + \$2.75}{13} + \dfrac{3\cdot\$4.75}{52} + \dfrac{\$6.00}{52} + \dfrac{10\cdot(-\$1.75)}{13}[/tex]
[tex]\Bbb E[W] \approx \boxed{-\$0.67}[/tex]
A group of 65 baseball players were surveyed about which hand they favor for batting. The data from the survey are shown in the Venn diagram.
Determine the value for each variable in the two-way table.
a =
b =
c =
d =
e =
The value of each variable in the two-way table is:
a = 7
b = 31
c = 28
d = 13
e = 65
What are the value of the variables?A Venn diagram uses circles that overlap each other to show logical relationships between two or more sets of items. A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns.
The following have to be established:
a player can either be male or female
a player favors either the left or the right
a = females that favor the left. Looking at the Venn diagram, this number is 7.
b = total number of females : 24 + 7 = 31
c = males that favor the right = total number of males - males that favor the left
34 - 6 = 28
d = Total number of people who favor the left = 7 + 6 = 13
Total number of baseball players = 65
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PLEASE HELP W THIS MATH QUESTION. correct answers only please
The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.
What is the quadratic equation behind two circular sections of equal area?
Herein we have two circular sections of equal area, whose expressions are described by the following geometric equations:
Semicircle
A = 0.5π · x² (1)
Half Semicircle
A = 0.25π · (x + 2)² (2)
By equalizing (1) and (2):
0.5π · x² = 0.25π · (x + 2)²
2 · x² = (x + 2)²
2 · x² = x² + 4 · x + 4
x² - 4 · x - 4 = 0
x² - 4 · x + 4 = 8
(x - 2)² = 8
x - 2 = ±√8
x = 2 ± √8
x = 2 ± 2√2
x = 2 · (1 ± √2)
x = 2 · (1 ± 1.41)
x₁ = 2 · 2.41 ∨ x₂ = 2 · (- 0.41)
x₁ = 4.82 ∨ x₂ = - 0.82
The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.
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calculate the slope of the line in the graphs and show your work
calculate the slope of a line that passes through (1,4) and (5,8)
Answer:
7.a) 5
7.b) 1/2
8. 1
Step-by-step explanation:
7.
a)
Read the points on the graph (0, 0) and (1, 5).
slope = (5 - 0)/(1 - 0) = 5/1 = 5
b)
read the points on the graph (0, 0) and (4, 2).
slope = (2 - 0)/(4 - 0) = 2/4 = 1/2
8.
Points (1, 4) and (5, 8)
slope = (8 - 4)/(5 - 1) = 4/4 = 1
Sloane kicked a soccer ball off the ground at a speed of 36 feet per second. the height of the ball can be represented by the function h(t) = −16t2 36t where t is the time in seconds. . how many seconds did the ball travel before returning the ground? t = 0.44 seconds t = 2.25 seconds t = 16 seconds t = 36 seconds
The total time in seconds the ball will take to travel before returning the ground is 2.25 seconds.
What is factorisation?The breaking or breakdown of an entity (such as an integer, a matrices, or a polynomials) into a products of another unit, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring in mathematics.
Calculation for the time;
Let 't' be the time in second the ball will travel.
Let H(t) be the total height travelled by the ball.
The equation of the height is given as
[tex]H(t)=-16 t^{2}+36 t[/tex]
As soon as the ball will return to the ground the total height will become zero.
So, put equation of height equal to zero.
[tex]-16 t^{2}+36 t=0[/tex]
Factorise the above equation;
[tex]-16 t\left(t-\frac{9}{4}\right)=0[/tex]
Put each value equals to zero to get the value of time.
[tex]\begin{aligned}&t=0 \mathrm{sec} \\&t=9 / 4=2.25 \mathrm{sec}\end{aligned}[/tex]
As, time can not be zero
Therefore, the total time taken by the ball to return to the ground is 2.25 sec.
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Functions f(x) and g(x) are composed to form h (x) = startroot x cubed minus 2 endroot. if f (x) = startroot x 2 endroot and g (x) = x cubed a, what is the value of a?
Function Composition exists when two functions f(x) and g(x) result in another function h(x), such that h(x) = f(g(x)). For function composition h(x) = f(g(x)), the value of a exist -4.
What is function Composition?
Function Composition exists when two functions f(x) and g(x) result in another function h(x), such that h(x) = f(g(x)). In other words, put the outcome of one function into the other one.
Here, h(x) = f(g(x))
which means, h(x) = f(x³+ a)
[tex]$h(x) = \sqrt{x^3+a+2}[/tex]
[tex]$\sqrt{x^3-2} = \sqrt{x^3+a+2}[/tex]
To estimate the value of a, we separate equal terms:
1) Both are squared, so we can "eliminate" the square;
2) x³ = x³
3) -2 = a+2
a = -4
For function composition h(x) = f(g(x)), the value of a exist -4.
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Help!! PLSS
what can be to total of 100% if divided by four percentage?
__%
__%
__%
__%
=100%
Step-by-step explanation:
I am not sure I understand your question (grammatically).
percentages are like any other numbers. they can be added, divided, ...
so, 100% or simply 100 : 100/4 = 25.
so, 4×25 = 100.
and 4×25% = 100%
I am really not sure if this is your question, but it fits to your table with 4 entries and 100% as result.
The amount of unexplained variance in a relationship between two variables is called?
Answer:
The amount of unexplained variance in a relationship between two variables is called: coefficient of alienation also called coefficient of nondetermination. A positive correlation between two variables would be represented in a scatterplot as. line sloping upwards. .
Step-by-step explanation:
PLEASE HELP IM SO STUCK
Answer:
y-9=-4(x+2)
Step-by-step explanation:
The point-slope formula is:
y-y1=m(x-x1)
m=-4 and use the point (-2, 9)
x1 y1
Plug in the information.
y-9=-4(x+2)
This is the equation written in point-slope form using the point (-2, 9).
Hope this helps!
A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is 1.5. Use a level of significance of 0.01 to conduct a left-tailed test of the claim that the population mean is 9.2. Compute the sample test statistic t. 0.005 0.0005 -2.267 -3.267
No,the population mean is not equal to 9.2 and the value in t statistic is -1.02.
Given sample size of 49,sample mean of 8.5,standard deviation of 1.5, significance level of 0.01.
We are required to find out whether the population mean is equal to 9.2 and the value of t in test statistic.
We have to first make the hypothesis for this.
[tex]H_{0}[/tex]:μ≠9.2
[tex]H_{1}[/tex]:μ=9.2
We have to use z statistic because the sample size is more than 30.
Z=(X-μ)/σ
We have been given sample mean but we require population mean in the formula so we will use sample mean.
Z=(8.5-9.2)/1.5
=-0.7/1.5
=-0.467
P value of -0.467 is 0.67975.
P value is greater than 0.01 so we will accept the hypothesis means population mean is not equal to 9.2.
t=(X-μ)/s/[tex]\sqrt{n}[/tex]
=(8.5-9.2)/1.5/[tex]\sqrt{49}[/tex]
=-0.7/0.21
=-1.02
Hence it is concluded that no,the population mean is not equal to 9.2 and the value in t statistic is -1.02.
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Charlie throws a ball up into the air. while the ball is airborne, which is the greatest force acting on the ball to slow it down?
The greatest force acting on the ball to slow it down is Gravitational force.
Which forces will act on the ball?When ball is thrown upwards then there will be two forces on the ball opposite to the motion of ball
1. Gravitational force (mg)
2. Air friction or air drag
Both forces are opposite to the motion of the ball and it will cause the decrease in the speed of the ball.
Now here due to less value of drag coefficient on the ball we will say that ball will decrease its speed more due to gravitational force compare to friction force of air.
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add 5x+4y;3x-7y;-4x+8y
The answer is 4x + 5y.
Here, what needs to be done is to combine like terms.
5x + 4y + 3x - 7y - 4x + 8y5x + 3x - 4x + 4y + 8y - 7y4x + 5yThe formula f(x 1) = two-thirds(f(x)) defines a geometric sequence where f(1) = 18. which explicit formula can be used to model the same sequence?
The explicit formula is Tn = 18[[tex]\frac{2}{3} ^{n-1}[/tex]]
here, we have to find n.
Now, F(2) = 2/3 * f1 = 2/3 * 18 = 12
F(3) = 2/3 * f(2) = 2/3 * 12 = 8
F(4) = 2/3 * F(3) = 2/3 * 8 = 16/3
F(5) = 2/3 * 16/3 = 32/9
These equations form a pattern.
That is Tn = (2/3)^(n-1)(18)
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nts out of
10
Flag question
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
Surface Area:
Check
9 km.
7 km.
km²
6 km.
8 km.
11 km.
PLEASE HELP MEEEE
EXPLAIN
The Surface area of the triangular prism is: 318 km³.
What is a Triangular Prism?A triangular prism is a solid that has two triangular bases and three rectangular faces.
What is the Surface Area of a Triangular Prism?The surface area of a triangular prism is the sum of the areas of its two triangular bases and three rectangular faces.
The formula for the surface area of a triangular prism = (S1 +S2 + S3)L + bh, where:
Perimeter of the base = S1 + S2 + S3
Length of the prism = L
2 × Base Area = bh
Given the following:
s1 + s2 + s3 = 7 + 9 + 8 = 24 km
L = 11 km
bh = (9)(6) = 54 km²
Plug in the values
Surface area of the triangular prism = (24)11 + 54
Surface area of the triangular prism = 264 + 54
Surface area of the triangular prism = 318 km³
Thus, the Surface area of the given triangular prism in the diagram above is: 318 km³.
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s in
Squaring both sides of the equation
√√x+1=√x+6-1 and simplifying, the equation
becomes 3 = √√x+6.
The solution of the equation is
The value of x in given linear equation is x = 3.
According to the statement
we have given that the equation and we have to find the solution of that equation.
So, For this purpose,
The given equation is :
[tex]\sqrt{ x+1} = \sqrt{ x+6} -1[/tex]
From this equation it is clear that the it is a linear equation.
So, for find the value of x
To solve this equation squaring on both sides then equation become
x+1 = x+6 +1 -2√x+6.
Then
-2√x+6 = -6
then
[tex]\sqrt{x + 6} = 3[/tex]
Now remove the square by S.B.S.
Then the equation become
x +6 = 9
x = 3.
In this equation the value of x is 3.
So, The value of x in given linear equation is x = 3.
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Find the first four partial sums, s1,s2,s3,s4, and the nth partial sum of the squence an=log(nn+1).
The first four partial sums of the sequence are S₁ = 0.3010, S₂ = 0.9999, S₃ = 2.447, S₄ = 4.8569.
In this question,
A sequence is a set of things (usually numbers) that are in order. A partial sum is the sum of part of the sequence.
The sequence is [tex]a_{n} =log(n^{n}+1 )[/tex]
The first four partial sum S₁, S₂, S₃, S₄ can be calculated by substituting n = 1,2,3,4 in the sequence.
S₁ can be calculated as
S₁ = a₁
⇒ [tex]a_{1} =log(1^{1}+1 )[/tex]
⇒ [tex]a_{1} =log(1+1 )[/tex]
⇒ [tex]a_{1} =log(2 )[/tex]
⇒ [tex]a_{1} =0.3010[/tex]
Now, S₁ = 0.3010
S₂ can be calculated as
S₂ = a₁ + a₂
⇒ [tex]a_{2} =log(2^{2}+1 )[/tex]
⇒ [tex]a_{2} =log(4+1 )[/tex]
⇒ [tex]a_{2} =log(5 )[/tex]
⇒ [tex]a_{2} =0.6989[/tex]
Now, S₂ = 0.3010 + 0.6989
⇒ S₂ = 0.9999
S₃ can be calculated as
S₃ = a₁ + a₂ + a₃
⇒ [tex]a_{3} =log(3^{3}+1 )[/tex]
⇒ [tex]a_{3} =log(27+1 )[/tex]
⇒ [tex]a_{3} =log(28)[/tex]
⇒ [tex]a_{3} =1.4471[/tex]
Now, S₃ = 0.3010 + 0.6989 + 1.4471
⇒ S₃ = 2.447
S₄ can be calculated as
S₄ = a₁ + a₂ + a₃ + a₄
⇒ [tex]a_{4} =log(4^{4}+1 )[/tex]
⇒ [tex]a_{4} =log(256+1 )[/tex]
⇒ [tex]a_{4} =log(257 )[/tex]
⇒ [tex]a_{4} =2.4099[/tex]
Now, S₄ = 0.3010 + 0.6989 + 1.4471 + 2.4099
⇒ S₄ = 4.8569
Hence we can conclude that the first four partial sums of the sequence are S₁ = 0.3010, S₂ = 0.9999, S₃ = 2.447, S₄ = 4.8569.
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Question 7(Multiple Choice)
(05.02 MC)
Which expression is equivalent to 3 log2 x - 4 log2 y + 2 log2 z?
Answer:
C.) [tex]log_2(\frac{x^3z^2}{y^4})[/tex]
Step-by-step explanation:
To find the answer, you need to simplify the expression. To do so, you must combine the logs. You can combine the logs because they all have the same subscript (2).
[tex]3 log_2x - 4log_2y + 2log_2z[/tex] <----- Given expression
[tex]log_2x^3-log_2y^4+log_2z^2[/tex] <----- Raise coefficients to variables
[tex]log_2x^3+log_2z^2-log_2y^4[/tex] <----- Rearrange
[tex]log_2(x^3z^2)-log_2y^4[/tex] <----- Multiply added logs
[tex]log_2(\frac{x^3z^2}{y^4})[/tex] <------ Divide subtracted log
Express the multiplication of a logarithm number of an expression as the logarithm of the power of the expression.
㏒₂ x³ - ㏒₂ y⁴ + ㏒₂ z²Take the product of the arguments
[tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ Log_{2} \frac{x^{3}z^{2} }{y^{4} } } }}}}[/tex]
Therefore, the correct option is alternative "C".
