The mean and standard deviation for the GPA of the students will be 3 and 0.8165.
How to calculate the mean?The mean simply means the average of a given set of numbers. The mean will be:
= 12/4
= 3
The standard deviation will be:
= ✓2/3
= 0.8165
The 95% confidence interval for the populations mean GPA will be 1.70 < U < 4.30. The interval lower limit is:
= 3.00 - 1.299.l
= 1.70
The interval upper limit will be;
= 3.00 + 1.299
= 4.30
Also, the regression line is Y = -1.2857 + 0.3571x.
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Write each of the following expressions as a^n or a^n b^m,
Step-by-step explanation:
[tex]2 {}^{2} \times 2 {}^{3} \times 2 {}^{1} \times 3 {}^{ - 1} {}^{ (- 2)} [/tex]
[tex]2 {}^{6} 3 {}^{2} [/tex]
please need help involve steps for better understanding conic section
Which number line shows the solutions to x > 5?
OA. 8642 8 2 4 6 8
OB. 864-2 0 2 4 6 8
8-64-202468
4-202468
D. Pls help
Answer:
b.
Step-by-step explanation:
The inequality says that x is bigger than 5. The number line shows the arrow starting from 5 and going bigger. Therefore, that number line is correct.
HELPPP!!
Statement:
Some whole numbers are
irrational numbers.
True or False?
Some rational numbers are not whole numbers.
True or False?
Some irrational numbers are not integers.
True or False?
All rational numbers are integers.
Answer:
Step-by-step explanation:
Comment
A rational number is one that can be expressed as x/y. The first statement is false. All whole numbers are rational. They can always be expressed as x/1
Some rational numbers are not whole numbers. That's true. 4/7 is rational but not whole.
Some irrational numbers are not integers. I'm tempted to say this is true.
pi is irrational and it certainly is not an integer.
Answer
false
true
true.
Write a sine function that has an amplitude of 5, a midline of 4 and a period of
4
Answer:
See below
Step-by-step explanation:
Start with sin x
amplitude of 5
5 sin x
midline 4
5 sin (x) + 4
period of 4
2 pi / 4 = pi/2
5 sin ( x pi/2 ) + 4
A train travels 80 mph for 2 hours and then it travels 60 mph for 3 hours . What is its average speed over the entire 5-hour trip?
Answer:
68 mph
Step-by-step explanation:
80 m/hr * 2 hr = 160 miles
60 m/hr * 3 hr = 180 miles
total miles / total time = average speed
340 miles / 5 hr = 68 m p h
The financial planner for a beauty products manufacturer develops the system of equations below to determine how many combs must be sold to generate a profit. the linear equation models the income, in dollars, from selling x plastic combs; the quadratic equation models the cost, in dollars, to produce x plastic combs. according to the model, for what price is each comb being sold? startlayout enlarged left-brace 1st row y = startfraction x over 2 endfraction 2nd row y = negative 0.03 (x minus 95) squared 550 $0.03 $0.50 $0.95 $2.00
The price of each comb is $0.5, if the linear equation y = x/2 models the income, in dollars, from selling x plastic combs
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
Profit = income - cost
Given that the linear equation y = x/2 models the income, in dollars, from selling x plastic combs. Hencee:
Price of each comb = (x/2) / x = 0.5
The price of each comb is $0.5, if the linear equation y = x/2 models the income, in dollars, from selling x plastic combs
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Answer:
$0.50
Step-by-step explanation:
The answer above is correct.
If function f : R --> R where f(X)=X³ - kX² + 12X - 7 is a one to one function, then k belongs to....
Since f(x) is a cubic polynomial, it has at most 3 distinct roots. If f(x) has 3 real roots, then f(x) = 0 for more than one instance of x.
But if f(x) is one-to-one, then there must be only one real root and the other two are non-real. Let a + bi and a - bi be these non-real roots and c the single real root; then we can factorize f(x) as
[tex]f(x) = x^3 - kx^2 + 12x + 7 = (x - (a + bi)) (x - (a - bi)) (x - c)[/tex]
Expand the right side to get
[tex]f(x) = x^3 - kx^2 + 12x + 7 = (x^2 - 2ax + a^2+b^2) (x - c)[/tex]
[tex]f(x) = x^3 - kx^2 + 12x + 7 = x^3 - (2a + c) x^2 + (a^2 + 2ac + b^2) x - (a^2c + b^2c)[/tex]
from which it follows that
[tex]\begin{cases}k = 2a + c \\ 12 = a^2+2ac+b^2 \\ 7 = -a^2c-b^2c\end{cases}[/tex]
Since f(x) has only one root, its graph will have no turning points/extrema. If f(x) has a critical point, it must be a saddle point. Differentiating f(x) yields
[tex]f'(x) = 3x^2 - 2kx + 12[/tex]
Solve for the critical point:
[tex]f'(x) = 3x^2 - 2kx + 12 = 0[/tex]
[tex]x^2 - \dfrac{2k}3 x = -4[/tex]
[tex]x^2 - \dfrac{2k}3 x + \dfrac{k^2}9 = \dfrac{k^2}9-4[/tex]
[tex]\left(x - \dfrac k3\right)^2 = \dfrac{k^2}9-4[/tex]
[tex]x = \dfrac k3 \pm \sqrt{\dfrac{k^2}9-4}[/tex]
There is at most one real critical point, so either the square root term vanishes or it produces a non-real number. This happens for
[tex]\dfrac{k^2}9 - 4 \le 0 \implies k^2 \le 36 \implies -6 \le k \le 6[/tex]
So, if f(x) is one-to-one, then
[tex]k \in \left\{\kappa \in \Bbb R \mid -6 \le \kappa \le 6\right\}[/tex]
5) In the segment below, segment DC = 29,
lengths AB, BC, AC, rounded to the nearest tenth, and angle measures for
Applying the trigonometric ratios and the triangle sum theorem, the missing lengths and angles are:
AB = 27.2 units
BC = 33.5 units
AC = 50.4 units.
m∠A = 38°
m∠ABC = 112°
What are the Trigonometric Ratios?The trigonometric ratios, SOHCAHTOA, are used to find the sides or angles of a right triangle.
Find BD using TOA:
tan ∅ = opp/adj
tan 30 = BD/29
BD = tan 30 × 29
BD = 16.7 units
Find AD using TOA:
tan ∅ = opp/adj
tan 52 = AD/16.7
AD = (tan 52)(16.7)
AD = 21.4 units
Find AB using SOH:
sin 52 = 21.4/AB
AB = 21.4/sin 52
AB = 27.2 units
Find BC using CAH:
cos 30 = 29/BC
BC = 29/cos 30
BC = 33.5 units
Find AC:
AC = AD + DC
AC = 21.4 + 29
AC = 50.4 units.
m∠A = 180 - 52 - 90 = 38° (triangle sum theorem)
m∠ABC = 180 - m∠A - m∠C (triangle sum theorem)
m∠ABC = 180 - 38 - 30
m∠ABC = 112°
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A small ranch is 0.4 of an acre. There is 0.2 of the piece of land that is used for vegetable crops. What part of the land is used for
the vegetable crops?
A. 0.12 of an acre
B. 0.08 of an acre
C. 0.18 of an acre
D. 0.06 of an acre
I WILL MARK YOU AS BRAINLESS IF YOU PLEASE HELP ME!!
Answer:
Correct answer is B. 0.08
Step-by-step explanation:
Help Me, I only have 2 minutes
Answer:
[tex]6 \frac{2}{13} [/tex]
I need help with (ii) both (a) and (b) thanks
Answer:
(i) 126 ways
(ii)
(a) 1/126
(b) 5/14
Step-by-step explanation:
(i) Possible selections
⁹C₄ = 9! / 5! 4!9 x 8 x 7 x 6 x 5! / 5! x 4 x 3 x 2 x 172 x 7 x 6 / 247 x 6 x 342 x 3126 ways(ii) (a) all girls
⁴C₄ 4! / 1! 4!1 wayP = 1/126(ii) (b) more boys than girls
3 boys, 1 girl⁵C₃ x ⁴C₁(5! / 2! 3!) x (4! / 3! 1!)(5 x 4 x 3!/ 2 x 3!) x (4 x 3! / 3!)10 x 440 ways2. 4 boys, no girls
⁵C₄5! / 1! 4!5 x 4! / 4!5 ways⇒ 40 + 5 = 45 ways
⇒ P = 45/126 = 15/42 = 5/14
The probability of guessing on four true and false questions and getting all four questions correct
Answer:
50-50
Step-by-step explanation:
If yoiu have 4 and divide it b
Write the equation of the circle graphed below
Answer:
were is the circle to be to be equated
The table below shows the number of marbles of different colors in a bag:
Marble Experiment
Color of
Marbles Number of
Marbles
Red
5
White
8
Black
2
Deja draws a marble from the bag randomly without looking. She then draws another marble from the bag without replacing the first one. Which expression shows the probability of drawing red marbles in both the trials?
5 over 15 multiplied by 4 over 14
5 over 15 multiplied by 4 over 15
5 over 15 added to 4 over 14
5 over 15 added to 4 over 15
Answer:
[tex]\huge\boxed{\sf \frac{5}{15} + \frac{4}{14} }[/tex]
Step-by-step explanation:
Formula for probability: [tex]\boxed{\displaystyle Probability = \frac{number\ of\ possible\ outcomes}{total\ number\ of \ outcomes} }[/tex]Solution:Total number of marbles = 5 + 8 + 2 = 15
Number of red marbles = 5
Probability to draw a red marble at the first trial = 5/15
Number of marbles left = 15 - 1 = 14
Number of Red marbles left = 5 - 1 = 4
Probability to draw a red marble at the second trial = 4/14
Total probability:[tex]\displaystyle =Probability \ of \ drawing \ a \ red \ marble \ at \ the \ (second \ attempt +first \ attempt)\\\\= \frac{5}{15} + \frac{4}{14} \\\\\rule[225]{225}{2}[/tex]
3. If 3, x, y, 18, are in arithmetic progression, (A, P) find the value of x and y
b) the sum of the second and third terms of a geometric progression is six times the fourth term, find the two possible values of common ratio
i) If the seconds term is 8 and the common ration is positive, find the first six terms. 10mrks
Answer:
Below in bold
Step-by-step explanation:
The sequence is:
3, x, y, 18
If this is an A P then
x - 3 = y - x
2x - y = 3 (A) and
y - x = 18 - y
2y - x = 18 (B)
Multiply (A) by 2:
4x - 2y = 6 (C)
Adding B and C:
3x = 24
x = 8.
and
2y - 8 = 18
2y = 26
y = 13.
So x = 8 and y = 13.
b) ar + ar^2 = 6ar^3 where a = first term and r = common ratio
Divide by a:
r + r^2 = 6r^3
6r^3 - r^2 - r = 0
r(6r^2 - r - 1) = 0
r(3r + 1)(2r - 1) = 0
So the 2 possible values of r
= -1/3 and 1/2.
i) The common ratio is positive so it must be 1/2.
Second term ar = 8
1/2 a = 8
a = 16.
So the first 6 terms are:
16, 8, 4, 2, 1, 1/2.
Given that A = {1, 2, 3, 4, 5, 6] maps respectively to B = {3, 4, 5, 6, 7, 8). Find an injective function f(x) such that f: A → B. Hint: Can you depict any relationship between sets A and B?
Answer: f(x) = x + 2
Step-by-step explanation:
A = {1, 2, 3, 4, 5, 6]
B = {3, 4, 5, 6, 7, 8)
for each A, B is 2 more
f(1) = 1 + 2 = 3
f(2) = 2 + 2 = 4
f(3) = 3 + 2 = 5
and so on...
⇒ f(x) = x + 2
Function ggg can be thought of as a scaled version of f(x)=x^2f(x)=x
2
f, left parenthesis, x, right parenthesis, equals, x, squared.
A parabola labeled f represents the equation y equals x squared. A parabola labeled g passes through the point negative 1, 4, through the origin, and through the point 1, 4.
Write the equation for g(x)g(x)g, left parenthesis, x, right parenthesis.
Using translation concepts, it is found that the equation for function g(x) is given by:
g(x) = 4x².
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is given by:
f(x) = x².
This function passes through point (1,1). Function g(x) passes through point (1,4), that is, it is horizontally compressed by a factor of 4, hence g(x) is given by:
g(x) = 4x².
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Please help me with those questions as soon as possible
Help me please!!!!!!
1.a. Typical number chosen = the median value = 6
b. 27
2. a. 21
b. b. How the scores vary = Range of the scores = 5
c. Mode = 8
d. Median = 8
What is the Range, Mode, and Median of a Data Set?Range = Highest value - least value
Mode = most occurred data point
Median = center value of the data distribution (typical value of a dot plot).
1. a. Typical number chosen = the median value (center value) on the dot plot = 6
b. The number enrolled = number of student represented on the dot plot + 2 students absent = 25 + 2 = 27.
2. Data given: 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10
a. There are 21 data points given, therefore, the number of students in the afternoon math class is: 21.
b. How the scores vary = Range of the scores = 10 - 5 = 5
c. Mode of the data = 8
d. Median score = 8
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hi! i cant find the answer on brainly for these questions!
a. 10- 4/10=?
b. 25- 3/25=?
c. 105- 84/84
d. 170- 125/125
thnx!
Answer:
a. 10 - [tex]\frac{2}{5}[/tex] = [tex]9\frac{3}{5}[/tex] or 9.6
b. 25 - [tex]\frac{3}{25}[/tex]= [tex]24 \frac{22}{25}[/tex] or 24.88
c. 105-[tex]\frac{84}{84}[/tex] = 104.0
d. 170 - [tex]\frac{125}{125}[/tex] = 169.0
A children’s news and talk show is broadcasted for 2 hours each weekday. On Saturdays and Sundays, the show is an hour longer than during the week. How many hours is this show broadcasted each week?
ANSWER QUICK SUPER EASY 99 PTS I JUST DONT REMEMBER
Find the value of tan θ, if cos θ =
Answer:
B
Step-by-step explanation:
Given the function f(x) = (1/4)^x , how will g(x) = (1/4) ^x-3 + 5 be translated
See
x is decreased by 3 .
and y is increased by 5
So translation is
f(x)=(1/4)^xHence
f(x)=(1/4)^x-3+5So
x will go 3 units right
y will go 5units up
Graph attached
Answer:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function:
[tex]f(x)=\left(\dfrac{1}{4}\right)^x[/tex]
Translated 3 units to the right:
[tex]f(x-3)=\left(\dfrac{1}{4}\right)^{x-3}[/tex]
Translated 5 units up:
[tex]f(x-3)+5=\left(\dfrac{1}{4}\right)^{x-3}+5[/tex]
[tex]\implies g(x)=f(x-3)+5[/tex]
Therefore:
[tex]\textsf{g(x) is a translation of f(x) by }\left(\begin{array}{c}3\\5\\\end{array}\right)[/tex]
i need help with it pls
Answer:
Step-by-step explanation:
Step 1: What are the couch's original coordinates?
A: (-4, 2)N: (-4, 3)G: (-1, 3)L: (-1, 4)E: (-5, 4)S: (-5, 2)Step 2: Rotate the couch 90° counterclockwise.
Rule: (x, y) → (-y, x)
A': (-4, 2) → (-2, -4)N': (-4, 3) → (-3, -4)G': (-1, 3) → (-3, -1)L': (-1, 4) → (-4, -1)E': (-5, 4) → (-4, -5)S': (-5, 2) → (-2, -5)Step 3: Now reflect the "new" couch over the y-axis.
Rule: (x, y) → (-x, y)
A'': (-2, -4) → (2, -4)N'': (-3, -4) → (3, -4)G'': (-3, -1) → (3, -1)L'': (-4, -1) → (4, -1)E'': (-4, -5) → (4, -5)S'': (-2, -5) → (2, -5)Step 4: Finally translate the new new" couch right 1 unit and up 5 units.
Rule: (x + 1, y + 5)
A''': (2, -4) → (2 + 1, -4 + 5) → (3, 1)N''': (3, -4) → (3 + 1, -4 + 5) → (4, 1)G''': (3, -1) → (3 + 1, -1 + 5) → (4, 4)L''': (4, -1) → (4 + 1, -1 + 5) → (5, 4)E''': (4, -5) → (4 + 1, -5 + 5) → (5, 0)S''': (2, -5) → (2 + 1, -5 + 5) → (3, 0)Step 5: Use the distance formula to show that the length of EG is the same as the length of E'''G'''.
EG: (-5, 4)(-1, 3) E'''G''': (5, 0)(4, 4)Distance between E(-5, 4) and G(-1, 3)
x₁ = -5x₂ = -1y₁ = 4y₂ = 3[tex]\large \textsf {d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$}\\\\\large \textsf {d = $\sqrt{(-1-(-5))^2+(3-4)^2}$}\\\\\large \textsf {d = $\sqrt{(-1+5)^2+(3-4)^2}$}\\\\\large \textsf {d = $\sqrt{4^2+(-1)^2}$}\\\\\ \large \textsf {d = $\sqrt{16+1}$}\\\\\large \textsf {d = $\sqrt{17}$}\\\\\large \textsf {d = ${4.12}$}[/tex]
Distance between E'''(5, 0) and G'''(4, 4)
x₁ = 5x₂ = 4y₁ = 0y₂ = 4[tex]\large \textsf {d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$}\\\\\large \textsf {d = $\sqrt{(4-5)^2+(4-0)^2}$}\\\\\large \textsf {d = $\sqrt{(-1)^2+4^2}$}\\\\\large \textsf {d = $\sqrt{1+16}$}\\\\\ \large \textsf {d = $\sqrt{17}$}\\\\ \large \textsf {d = ${4.12}$}[/tex]
This means that the length of EG is the same as the length of E'''G'''.
Hope this helps!
Which number is a solution of the inequality x <-4? Use the number line to help answer the question. Number line starts like and ends like “ -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1. “
Netflix is considering a new romcom (romantic comedy) series. Before making a final decision, the producers design an experiment to estimate the proportion of viewers who would watch the series. A random sample of 1,000 viewers was selected and asked to watch the first two episodes. After viewing the episodes, 625 viewers indicated they would watch the new series. (Use t Distribution Table & z Distribution Table.) (Round your answers to 3 decimal places.)
Required:
a. Estimate the value of the population proportion of people who would watch the new series.
b. Develop a 99% confidence interval for the population proportion of people who would watch the new series.
A) the value of the population proportion of people who would watch the new series is 5 out of 8 viewers, and B) a 99% confidence interval for the population proportion of people who would watch the new series indicates that between 61.87% and 63.13% of viewers will watch the new series.
ProportionsGiven that Netflix is considering a new romcom (romantic comedy) series, and a random sample of 1,000 viewers was selected and 625 viewers indicated they would watch the new series, for A) estimate the value of the population proportion of people who would watch the new series, and B) develop a 99% confidence interval for the population proportion of people who would watch the new series, the following calculations must be made:
A)
625 = 1
1000 = X
1000 / 625 = X
1.6 = X
10 out of 16, or 5 out of 8.
B)
62.5 x 0.99 = 61.875
62.5 x 1.01 = 63.125
Therefore, A) the value of the population proportion of people who would watch the new series is 5 out of 8 viewers, and B) a 99% confidence interval for the population proportion of people who would watch the new series indicates that between 61.87% and 63.13% of viewers will watch the new series.
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In the given right triangle, write all trigonometric ratios ?
Answer:
see below
Step-by-step explanation:
You will need the hypotenuse 12 ^2 + 9^2 = h^2 h = 15
In a right triangle:
S O H C A H T O A
sin s = S A H = Opposite / Hypotenuse = 12/15
cos r = C A H = Adjacent / Hypotenuse = 12/ 15
Tan s = T O A = 12 / 9
cos (theta) = cos s = 9 / 15
Tan r = 9/12
arc cos(theta) = theta = arccos(9/15) = 53.13 degrees
A formation is:
A. Closing in on players so they do not have any room to maneuver
B. Mirroring the format and positioning of the other team
C. Marking and defending a specific area
D. An organized patter of player positions.
How many edges does the following shape have?
Answer:
6
Step-by-step explanation:
please help due in 10 mins
Answer:
the answers is -4 for this exerxises