Answer:
a. [tex]\mathtt{P(X \geq 25) =0.0170}[/tex] ( to four decimal places)
b. [tex]P(22.5<X<25) = 0.9043[/tex] ( to four decimal places )
c. The limits will be between the interval of ( 22.33,24.67 )
Step-by-step explanation:
Given that :
mean = 23.50
standard deviation = 5.00
sample size = 50
The objective is to calculate the following:
(a) What is the likelihood the sample mean is at least $25.00?
Let X be the random variable, the probability that the sample mean is at least 25.00 is:
[tex]P(X \geq 25) = 1 - P(\dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{25- 23.50}{ \dfrac{5}{\sqrt{ 50}} })[/tex]
[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5}{ \dfrac{5}{7.07107}} })[/tex]
[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5 \times 7.071}{ {5}})[/tex]
[tex]P(X \geq 25) = 1 - P(Z< 2.1213)[/tex]
[tex]P(X \geq 25) = 1 - P(Z< 2.12)[/tex] to two decimal places
From the normal tables :
[tex]P(X \geq 25) = 1 - 0.9830[/tex]
[tex]\mathtt{P(X \geq 25) =0.0170}[/tex] ( to four decimal places)
(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00?
[tex]P(22.5<X<25) = P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{25-23.5}{\dfrac{5}{\sqrt{50}}} ) - P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{22.5-23.5}{\dfrac{5}{\sqrt{50}}} )[/tex]
[tex]P(22.5<X<25) = P(Z<\dfrac{1.5}{\dfrac{5}{7.071}} ) - P(Z<\dfrac{-1}{\dfrac{5}{7.071}} )[/tex]
[tex]P(22.5<X<25) = P(Z<2.12) - (Z<-1.41 )[/tex]
[tex]P(22.5<X<25) = (0.9830 ) - (0.0787)[/tex]
[tex]P(22.5<X<25) = 0.9043[/tex] to four decimal places
(c) Within what limits will 90 percent of the sample means occur?
At 90 % confidence interval, level of significance = 1 - 0.90 = 0.10
The critical value for the [tex]z_{\alpha/2} = 0.05[/tex] = 1.65
Standard Error = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
Standard Error = [tex]\dfrac{5}{\sqrt{50}}[/tex]
Standard Error = 0.7071
Therefore, at 90 percent of the sample means, the limits will be between the intervals of : [tex](\mu \pm z_{\alpha/2} \times S.E)[/tex]
Lower limit = ( 23.5 - (1.65×0.707) )
Lower limit = ( 23.5 - 1.16655 )
Lower limit = 22.33345
Lower limit = 22.33 (to two decimal places).
Upper Limit = ( 23.5 + (1.65*0.707) )
Upper Limit = ( 23.5 + 1.16655 )
Upper Limit = 24.66655
Upper Limit = 24.67
The limits will be between the interval of ( 22.33,24.67 )
BRAINLIEST, 5 STARS AND THANKS IF ANSWERED BOTH CORRECTLY. 1. What is the 8th term of the following geometric sequence? -8, 24, -72, 216.. A. 52, 488 B. 5,832 C. 17,496 D. -17,496 ---------- 2. What is the 6th term of the following geometric sequence? 2, -14, 98, -686... A. 33,614 B. -33,614 C. 235,298 D. -235,298
Answer:
C; B
Step-by-step explanation:
The direct/explicit formula for a geometric sequence is the following:
[tex]a_n=a(r)^{n-1}[/tex]
Where aₙ represents the term n, a represents the initial value, and r represents the common ratio.
Therefore, to find the nth term, we just need to find the initial value and the common ratio.
1)
-8, 24, -72, 216...
The common ratio is the ratio between each consecutive term. Do two to confirm that they are indeed the same. Thus:
[tex]r=24/-8=-3\\r=-72/24\stackrel{\checkmark}{=}-3[/tex]
So, the common ratio is -3. And the initial value is -8. Thus, putting them into our equation:
[tex]a_n=-8(-3)^{n-1}[/tex]
Thus, the eighth term will be:
[tex]a_8=-8(-3)^{8-1}\\a_8=-8(-3)^7\\a_8=17496[/tex]
C
2)
Again, find the common ratio.
2, -14, 98, -686...
[tex]-14/2=-7\\98/-14\stackrel{\checkmark}{=}-7[/tex]
The common ratio is -7. The initial value is 2. Thus:
[tex]a_n=2(-7)^{n-1}[/tex]
And the sixth term will be:
[tex]a_6=2(-7)^{6-1}\\a_6=2(-7)^5\\a_6=-33614[/tex]
B
Please please please please help
Answer:
[tex]10 {x}^{2} + ( - 18)[/tex]
Step-by-step explanation:
Inserting fx into gx we get
[tex]5(2 {x}^{2} - 5) + 7[/tex]
Which then becomes
[tex]10 {x}^{2} - 25 + 7[/tex]
And finally the answer is
[tex]10 {x}^{2} - 18[/tex]
determine the equation for the quadratic relationship graphed below.
Answer:
[tex]\large \boxed{\sf \bf \ \ y=3x^2-6x-1 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
We can read from the graph that the vertex is (1,-4) , it means that the equation is, a being a real number.
[tex]y=a(x-1)^2-4[/tex]
And the point (0,-1) is on the graph so we can write.
[tex]a\cdot 1^2-4=-1 \\\\a-4+4=-1+4\\\\a = 3[/tex]
So the equation is.
[tex]y=3(x-1)^2-4\\\\=3(x^2-2x+1)-4\\\\=3x^2-6x+3-4\\\\=3x^2-6x-1\\\\=\boxed{3}x^2\boxed{-6}x\boxed{-1}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
[tex]y=3x^{2} -6x-1[/tex]
Step-by-step explanation:
The lines on a 2-cup liquid measuring cup divide each cup into eighths. If you measure 1 3/4 cups of water, between which two quantities can you be certain that your exact measurement will be?
Answer:
1 3/4 cups is between the 13th and 15th lines from the bottom.
Step-by-step explanation:
The bottom of the cup has no line and corresponds to 0 eights.
1st line up: 1/8 cup
2nd line up: 2/8 cup this is also called 1/4 cup
3rd line up: 3/8 cup
4th line up: 4/8 cup this is also called 1/2 cup
5th line up: 5/8 cup
6th line up: 6/8 cup this is also called 3/4 cup
7th line up: 7/8 cup
8th line up: 8/8 cup this is also called 1 cup
9th line up: 9/8 cup
10th line up: 10/8 cup this is also called 1 1/4 cup
11th line up: 1 3/8 cup
12th line up: 1 4/8 cup this is also called 1 1/2 cup
13th line up: 1 5/8 cup
14th line up: 1 6/8 cup this is also called 1 3/4 cup
15th line up: 1 7/8 cup
16th line up: 1 8/8 cup this is also called 2 cups
1 3/4 cups is between the 13th and 15th lines from the bottom.
Match each system of linear equations with the correct number of solutions
Answer:
Hey there!
The first equation has no solutions, as it is parallel lines.
The second equation has infinitely many solutions, as it is basically the same line, and the two lines intersect at infinite points.
The third equation is just one solution.
Let me know if this helps :)
Answer:
1 - No solution
2 - Infinitely many solutions
3 - One solution
Step-by-step explanation:
Hey there!
Well to find if there is no solution, one solution, or infinitely many we need to look at the slope and y intercept.
1) - No solution
This is no solution because both slopes are the same meaning they are parallel meaning they have no solution.
2) - Infinitely many solutions
We need to convert into slope-intercept.
y = -x + 4
y = -x + 4
Since both slopes and y-intercepts are the same they overlap meaning they have infinite solutions.
3) - One solution
Slope-intercept,
y = -3x + 11
y = -1/3x + 1/3
Because both slopes are y-intercepts are different they have only one solution.
Hope this helps :)
The projected worth (in millions of dollars) of a large company is modeled by the equation w = 206(1.1) t. The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2011? A. 10%; $534.31 million B. 11%; $646.52 million C. 10%; $587.74 million D. 11%; $226.60 million
Answer:
Hey There!! The Correct answer is: The equation is w = 241(1.06)t
And here variable t represents the number of years since 2000.
In 2001 means t=2001 -2000 = 1
So we plug 1 for t in the given expression , that is w = 241(1.06)1 = 241 * 1.06 = 255.46
Therefore in 2001, it should be worth to 255.46.
And in the given expression 1.06=1 +0.06, where 0.06 is the annual percent of growth that is 6 % .
Hope It Helped!~ ♡
ItsNobody~ ☆
The projected annual percent of growth is 10% and the company worth in 2011 will be $587.74 millions. Then the correct option is C.
What is an exponent?Consider the function:
y = a (1 ± r) ˣ
Where x is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
If there is a plus sign, then there is exponential growth happening by r fraction or 100r %.
If there is a minus sign, then there is exponential decay happening by r fraction or 100r %.
The projected worth (in millions of dollars) of a large company is modeled by the equation is given as,
[tex]\rm w = 206\times (1.10)^t\\\\w = 206\times (1+0.10)^t[/tex]
Then the projected annual percent of growth is 10%.
The variable t represents the number of years since 2000.
Then the company worth in 2011 will be
w = 206 × 1.1¹¹
w = $587.74 millions
The projected annual percent of growth is 10% and the company worth in 2011 will be $587.74 millions.
Then the correct option is C.
More about the exponent link is given below.
https://brainly.com/question/5497425
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2c+17.6 =6 SOLVE --------------- 4 give your answer as a decimal get brainly
Answer:
[tex]\huge\boxed{x = -5.8}[/tex]
Step-by-step explanation:
2x + 17.6 = 6
Subtracting both sides by 17.6
2x = 6 - 17.6
2x = -11.6
Dividing both sides by 2
x = -11.6 / 2
x = -5.8
#1 why is it B？
No idea someone help plz
Answer:
Option (B)
Step-by-step explanation:
1). Given function is,
[tex]f(x)=\frac{1}{x-1}+3[/tex]
It the given function 'f' is transformed by a translation of 2 units to the right, the new function will be,
h(x) = f(x - 2)
h(x) = [tex]\frac{1}{(x-2)-1}+3[/tex]
= [tex]\frac{1}{x-3}+3[/tex]
Further the new function is translated by 6 units down,
g(x) = h(x) - 6
g(x) = [tex]\frac{1}{x-3}+3-6[/tex]
= [tex]\frac{1}{x-3}-3[/tex]
Since, transformed function 'g' passes through a point (x, -2),
g(x) = [tex]\frac{1}{x-3}-3[/tex]
-2 = [tex]\frac{1}{x-3}-3[/tex]
3 - 2 = [tex]\frac{1}{x-3}[/tex]
x - 3 = 1
x = 4
Therefore, Option (B) will be the answer.
Kim is buying an equal number of ounces of gummy bears and chocolate drops for her friends. Kim has $10 to spend at the store. If gummy bears cost $0.50 per ounce and chocolate drops cost $0.75 per ounce, how many ounces of each type of candy can she buy?
Answer:
she can buy 13.333 repeating ounces (13 as a full number) of chocolate drops or 20 ounces of gummy bears.
Step-by-step explanation:
take the amount of money you have, $10 and divide that by the price per ounce $10÷.5=20
Answer:
8 ounces
Step-by-step explanation:
Imagine X is the number of ounces she can buy for each type
.5 (x) the gummy and .75 (x) the chocolage = 10
combine like terms.
1.25 (X) = 10
X = 8
.5 (8) + .75(8) = 10
4+ 6 = 10
How many planes exist that pass through points A, B,
and C?
O
1
2
3
Answer: 1
Step-by-step explanation:
Given : A, B, c are three points.
We know that a plane exist that pass through three points.
So 1 plane exist that pass through points A, B, and C.
A point (gives location) , a line(gives length) and a plane(2 dimensional flat surface) are 3 undefined terms.
We need two points two make a line and three points to make a plane.
Answer:
Step-by-step explanation:
The answer is 1
If line ℓ is parallel to plane P, how many planes containing line ℓ can be drawn parallel to plane P?
Answer:
One
Step-by-step explanation:
Only one plane containing line ℓ can be drawn parallel to plane P
If two 2x2 matrices are inverses of each other, then multiplying them will result in what matrix below?
inverse of a matrix A is defined as [tex] AA^{-1}=I[/tex]
where I is the identity matrix of the respective order.
*Do the equations have solutions? x2=x
Answer:
x = 1
Step-by-step explanation:
x² = x
x² / x = 1
x = 1
Check:
1² = 1
50 POINTS! What is the product of complex conjugates? A. The product of complex conjugates is a difference of two squares and is always a real number. B. The product of complex conjugates is the same as the product of opposites. C. The product of complex conjugates is a sum of two squares and is always a real number. D. The product of complex conjugates may be written in standard form as a+bi where neither a nor b is zero. 2) The product (5+i)(5−i) is a real number, 26. What are the factors (5+i) and (5−i) called? A. imaginary numbers B. imaginary units C. complex conjugates D. complex numbers 3) What is the sum of the complex numbers −9−i and −5−i? A. 14+2i B. −14−2i C. −14+2i D. 14−2i 4) What is the product of the complex numbers 8i and 5i? A. 40i B. −40 C. −40i D. 40
Answer:
see below
Step-by-step explanation:
What is the product of complex conjugates?
( a+bi) (a-bi)
FOIL
a^2 -abi+abi -b^2i^2
a^2 + b^2
C. The product of complex conjugates is a sum of two squares and is always a real number.
What are the factors (5+i) and (5−i) called?
These are called complex conjugates because the imaginary parts are opposites
C. complex conjugates
What is the sum of the complex numbers −9−i and −5−i?
-9-i+-5-i
Add the real parts
-9-5 = -14
Add the imaginary parts
-i-i = -2i
-14-2i
B. −14−2i
What is the product of the complex numbers 8i and 5i?
8i*5i = 40 i^2
We know that i^2 = -1
40*-1 = -40
B. −40
if 13 minute video played for 6 minutes what is the amount of percent played
Answer: 46.15%
Step-by-step explanation:
From the question, we are informed that a 13 minute video played for 6 minutes. The amount of percent played will be:
= 6/13 × 100
= 0.4615 × 100
= 46.15%
what is the number of x
Answer:
X>4
Step-by-step explanation:
Solve for x: 2x+1= -3x+36
Answer:
x = 7
Step-by-step explanation:
2x + 1 = -3x + 36
2x + 3x + 1 = -3x + 3x +36
5x + 1 = 36
5x + 1 - 1 = 36 - 1
5x = 35
5x/5 = 35/5
x = 7
Answer:
first you would add 3x to -3x and 2x, then you would get 5x+1=36. Then you subtract 1 from 1 and 36. Then you get 5x=35. Then you divide by 5 to get the answer 7. so your answer is x=7
Step-by-step explanation:
hope this helps
Find the solution set for this equation M^2-4=0
Step-by-step explanation:
Hey, there !!
Let's simply work with it,...................
Here, theequation is,
[tex] {m }^{2} - 4 = 0 [/tex]
[tex]or \: {m }^{2} = 4[/tex]
[tex]or \: m = + - \sqrt{4} [/tex]
[tex]or \: m = + - \sqrt{ {2}^{2} } [/tex]
cancelling square and square root we get answer is,
= (+ - 2).
It means the value of m is plus(+) minus(-) 2.
Hope it helps...
What is the prime factorization of 270?
Answer:
[tex]\boxed{3^3 * 2 * 5}[/tex]
Step-by-step explanation:
Look at the image below ↓
Answer:
16 factors of 270
Step-by-step explanation:
1*270
2*135
3*90
5*54
6*45
9*30
10*27
15*18
How many more festivals had 18 to 23 countries represented than 0 to 5 countries represented?
Answer:
3
Step-by-step explanation:
Here, by reading the histogram, we will provide answer for the question asked.
We want to know how many more festivals had 18 to 23 countries represented than 0 to 5 countries.
Checking the histogram, we can see the 0-5 countries having a value of 1, while the 18-23 has a value of 4.
So, the number of more countries will be simply 4-1 = 3
Answer:
3
Step-by-step explanation:
D( Geese fly in V formation. The V forms a right angle that has 16 geese on 1 side and 12 geese on the other side. How many gesse would fill in the gap between the ends of each sides of the V formation?
Answer:
20 will fly in the missing side.
Step-by-step explanation:
This is a 90^o angle.
heres the formula for side c:
a^2 + b^2 = c^2
So,
12^2 + 16^2 = c^2
144 + 256 = c^2
square root of 400 = c
c = 20
So, 20 will fly in the missing gap of the V formation.
image is calculator.
Given: AB tangent at D, AD = OD = 4 Find: Area of the shaded region
Answer:
1.72
Step-by-step explanation:
AB tangent at D, AD = OD = 4
so triangle OAD is right angle with side of 4 and 4.
area of OAD = 1/2 * 4 * 4 = 8
Angle AOD = DAO = 45 deg.
so circular sector OCD area = area of circle O * 45/360
= pi * 4 * 4 * 45/360
= 2pi
Shade area ACD = trigangle OAD - circular sector OCD
= 8 - 2pi
= 1.72
Which is the length of the hypotenuse of the right triangle? Round your answer to the nearest tenth of a centimeter.
Answer:18.87
Step-by-step explanation:
to find the hypotenuse of a triangle, A^2 + B^2 = C^2 if A and B are sides and C is the Hypotenuse. 100 + 256 is 356, so C^2 is 356. to find C, we square root both sides. thus C^2 becomes C, and 356 becomes the square root of 356, which is 18.8679623... and rounded to the nearest 10th of a centimeter that's 18.87
Hope this helps!
Six times a number is greater than 20 more than that number
Answer:
4
Step-by-step explanation:
The answer is 4
Answer:
4
Step-by-step explanation:
4
PLEASE HELP DO TODAY IN A FRW MINUTESSS
You make a pattern bydrawing three similar rectangles. The widthof the smallest rectangle is45of the width ofthe medium-sized rectangle. The width ofthe medium-sized rectangle is45of thewidth of the largest rectangle. The largestrectangle is 12 inches long and 8 incheswide. Find the dimensions of the smallestrectangle. Explain your reasoning.
Answer:
5.12 in. by 7.68 in.
Step-by-step explanation:
In similar triangles, the ratios of the lengths of corresponding sides are equal.
width of medium triangle = 4/5 width of large triangle
width of medium triangle = 4/5(8 in.) = 6.4 in.
length of medium triangle = 4/5 length of large triangle
length of medium triangle = 4/5(12 in.) = 9.6 in.
width of small triangle = 4/5 width of medium triangle
width of small triangle = 4/5(6.4 in.) = 5.12 in.
length of small triangle = 4/5 length of medium triangle
length of small triangle = 4/5(9.6 in.) = 7.68 in.
Find the distance across the lake. Assume the triangles are similar.
80 m
х
у
20 m
60 m
Answer:
A. L = 240 m
Step-by-step explanation:
use similar triangle
L / 60 = 80 / 20
L = (80 * 60) / 20
L = 240 m
The required distance across the lake is 240 m. Hence correct option is A.
Similar triangles, are those triangles which have similar properties i.e. angles and proportionality of sides.
Since, triangles are similar.
The ratio of their sides are also equal
60/20= L/80
L=80 x 3
L = 240 m
Thus, the required distance across the lake is 240 m.
Learn more about similar triangles here:
brainly.com/question/25882965
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solve the following: - 3 raised to 1 by 5 the whole raised to 4 (3^1/5)^4
Answer:
8.30256
Step-by-step explanation:
Step 1: Write out expression
[tex]((-3)^{\frac{1}{5} })^{4(3^{\frac{1}{5} })^4[/tex]
Step 2: Use BPEMDAS to evaluate
[tex](-1.24573)^{4(3^{\frac{1}{5} })^4[/tex]
[tex](-1.24573)^{4(1.24573)^4[/tex]
[tex](-1.24573)^{4(2.40822)[/tex]
[tex](-1.24573)^{9.6329}[/tex]
= 8.30256
And we have our answer!
find square root of: 91+9, 47+2, 19+125, 9+0
Answer:
√(91+9)=√100
= 10
√(47+2)=√49
= 7
√(19+125)=√144
= 12
√(9+0)=√9
=3
What is a simpler form of the expression? -3(-4y+3)+7y please explain, i don’t understand it.
Answer:
19y - 9
Step-by-step explanation:
We can use the acronym PEMDAS. First, we need to calculate -3(-4y+3) by distributing. This is -3 * (-4y) + (-3) * 3 = 12y - 9 so the expression becomes 12y - 9 + 7y. Next, we need to combine like terms. 12y and +7y are like terms since they both have y so combining them gives us 12y + 7y = 19y. -9 stays by itself since there are no other constants so the final answer is 19y - 9.
Hey, it's really very easy to simplify .
I will write step by step.
Given:= -3 (-4y + 3) +7y
Now, let's Distribute:= (-3) (-4y) + (-3) (3) + 7y
= 12y + -9 + 7y
Now, Combine Like Terms:= 12y + -9 + 7y
= (12y + 7y) + (-9)
= 19y + -9Therefore, 19y + -9 is the answer.
