Answer:
The correct option is (C).
Step-by-step explanation:
The general form of a confidence interval is:
[tex]CI=SS\pm CV\cdot SE[/tex]
Here,
SS = Sample statistic
CV = critical value
SE = standard error
The width of the confidence interval is:
[tex]\text{Width}=2\cdot CV\cdot SE[/tex]
The width of the confidence interval is dependent upon the critical value and hence dependent upon the confidence level.
As the confidence level increases the critical value increases hence in turn increasing the width of the interval.
And as the confidence level decreases the critical value decreases hence in turn decreasing the width of the interval.
In this case the 95% confidence interval is, (90.21,100.37).
And the 99% confidence interval is, (93.61.98.53).
It is clear by looking at the two intervals that the 95% confidence interval is wider than the 99%. Thus, this clearly indicates that the co-worker made a mistake.
The correct option is (C).
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.) μ = 24; σ = 4.2 P(x ≥ 30) = ?
Answer:
Step-by-step explanation:
x is a random variable. Since we are assuming that x has a normal distribution, then we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 24
σ = 4.2
The indicated probability to be determined is P(x ≥ 30)
P(x ≥ 30) = 1 - P(x < 30)
For P(x < 30),
z = (30 - 24)/4.2 = 1.43
Looking at the normal distribution table, the probability corresponding to the z score is 0.9236
Therefore,
P(x ≥ 30) = 1 - 0.9236 = 0.0764
I NEED HELP PLEASE, THANKS! :)
Answer: C
Step-by-step explanation:
We can automatically eliminate D because since both matrices are 2x2, the product exists.
[tex]\left[\begin{array}{ccc}1&5\\-3&4\end{array}\right] \left[\begin{array}{ccc}2&6\\6&-1\end{array}\right] =\left[\begin{array}{ccc}1*2+5*6&1*6+5*(-1)\\(-3)*2+4*6&(-3)*6+4*(-1)\end{array}\right]=\left[\begin{array}{ccc}32&1\\18&-22\end{array}\right][/tex]
a classical music concert is to constist of 3 cello pieces, 3 choral works, and 3 pieces for piano. In how many ways can the program be arranged if a piano piece must come first
Answer:
120,960 ways
Step-by-step explanation:
Assuming that each piece is unique, then the order of each piece matters.
There are 9 pieces in total, there are 3 options for the first piece (3 piano pieces), and the remaining 8 pieces can be permuted. The number of possible arrangements is:
[tex]n=3*\frac{8!}{(8-8)!}\\ n=3*8*7*6*5*4*3*2*1\\n=120,960\ ways[/tex]
The program can be arranged in 120,960 ways.
Does anyone know how to solve this? I don't know how to type it out so Im gonna attach a pic
Answer:
tan =-1
Step-by-step explanation:
tan(θ)=sen(θ)/cos(θ)
so
[tex]tan(angle)=\frac{\frac{-\sqrt{2} }{2} }{\frac{\sqrt{2} }{2} } }\\\\tan(angle)=-1[/tex]
Answer:
Sin (theta)=[tex] - \frac{ \sqrt{2} }{2} [/tex]Tan ( theta)= [tex] - 1[/tex]Step-by-step explanation:
[tex]cos \: \: theta \: = \frac{ \sqrt{2} }{2} = \frac{1}{ \sqrt{2} } = cos \: \frac{\pi}{4 } [/tex]
[tex]cos \: (2\pi \: - \frac{\pi}{4} ) \: \: ( \frac{3\pi}{2} < theta < 2\pi)[/tex]
[tex] = cos \: \frac{7\pi}{4} [/tex]
Theta = 7π / 4
[tex]sin \: theta = sin \: \frac{7\pi}{4} [/tex]
[tex] = sin \: (2\pi \: - \frac{\pi}{4} )[/tex]
[tex] - sin \: \frac{\pi}{4} [/tex]
[tex] = \frac{ - 1}{ \sqrt{2} } [/tex]
[tex] = - \frac{ \sqrt{2} }{2} [/tex]
Finding tan theta:
[tex]tan \: theta = tan \: \frac{7\pi}{4} [/tex]
[tex] =tan \: (2\pi - \frac{\pi}{4} )[/tex]
[tex] = - tan \: \frac{\pi}{4} [/tex]
[tex] = - 1[/tex]
Hope this helps...
Good luck on your assignment...
Please answer this correctly
Answer:
0
Step-by-step explanation:
The probability of picking a even number is 1/3
If u don’t replace it then the probability of picking an even number is 0/3
Multiply and u get 0/9 or 0
Hope this helps
Answer:
0
Step-by-step explanation:
The number 2 is even.
The probability of picking an even number is 1/3.
You don't put the first card back.
1 and 3 are odd.
1/3 × 0 = 0
"a. How many study subjects were cases? b. How many study subjects were controls? c. What was the ratio of controls to cases?"
Answer:
The description is provided following.
Step-by-step explanation:
The given question is incomplete. The complete question will be:
Brain tumors No Brain tumors
Cell Phones 63 185
No Cell Phones 96 292
The further explanation is given below.
a...
Subjects with these symptoms/diseases are recognized as "cases." Consequently, the majority of the instances would be as follows:
⇒ [tex]63+96[/tex]
⇒ [tex]159[/tex]
b...
Subjects who might not have the disorder or infection are classified as "controls." Therefore, the amount of controls is as follows:
⇒ [tex]185+292[/tex]
⇒ [tex]477[/tex]
c...
The proportion of control and monitoring of instances:
⇒ [tex]\frac{478}{159}[/tex]
⇒ [tex]3.006[/tex]
Pls help me pick the right answer! Please
Simplify The square root of 5 (6-4 the square root of 3)
Answer:
7.75
Step-by-step explanation:
6-4=2
2 times the square root of 3=3.46410161514
square root of 5 times 3.46410161514=7.74596669242
to 2dp=7.75
Given the GCF or LCM, what else do you know about each pair of numbers?
a) Two numbers have a GCF of 2.
b) Two numbers have an LCM of 2.
c) Two numbers have a GCF of 3.
d) Two numbers have an LCM of 10.
Answer:
LCM is half of given product.GCF is half of given product. LCM is one-third of given product.GCF is one-tenth of given product.Step-by-step explanation:
We know that'
GCF × LCM = Product of given number
1. Two numbers have a GCF of 2
= 2 × LCM = Product of given number
LCM = Product of given number / 2
LCM is half of given product.
2. Two numbers have an LCM of 2
= GCF × 2 = Product of given number
GCF = Product of given number / 2
GCF is half of given product.
3. Two numbers have a GCF of 3
= 3 × LCM = Product of given number
LCM = Product of given number / 3
LCM is one-third of given product.
4. Two numbers have an LCM of 10
= GCF × 10 = Product of given number
GCF = Product of given number / 10
GCF is one-tenth of given product.
Simplify e^ln4
A. 1/4
B. 4
C. 1n4
D. E^4
Answer:
The answer is option B.
4Step-by-step explanation:
Using the expression
[tex] {e}^{ ln(x) } = x[/tex]
[tex] {e}^{ ln(4) } = 4[/tex]
Hope this helps you
Jennifer has carpet in her square bedroom. She decides to also purchase carpet for her living room which is rectangular in shape and 9 feet longer than her bedroom.
The area of the carpet required in the living room is given by the quadratic expression below, where x represents the side length, in feet, of the carpet in the bedroom.
X^2 + 9X
Match each part of the expression with what is represents.
Answer/Step-by-step explanation:
Let's highlight the dimensions of the bedroom and living room using the information given in the question:
==>Squared Bedroom dimensions:
Side length = w = x ft
Area = x*x = x²
==>Rectangular living room dimensions:
width = side length of the squared bedroom = x
length = (x + 9) ft
Area = L*W = x*(x+9) = x² + 9x
Now let's match each given expression with what they represent:
==>"the monomial, x, a factor of the expression x² + 9x" represents "the width of the carpet in the living room"
As we have shown in the dimensions of the squared bedroom above.
==>"the binomial, (x + 9), a factor of the expression x² + 9x" represents "the length of the carpet in the living room" as shown above in the dimensions for living room
==>"the second-degree term of the expression x² + 9x" represents "the area of the carpet in the bedroom"
i.e. the 2nd-degree term in the expression is x², which represents the area of the carpet of the given bedroom.
==>"the first-degree term of the expression x2 + 9x" represents "the increase in the area of carpet needed for the living room".
i.e. 1st-degree term in the expression is 9x. And it represents the increase in the area of the carpet for the living room. Area of bedroom is x². Area of carpet needed for living room increased by 9x. Thus, area of carpet needed for living room = x² + 9x
Each of 100 students in the Allen School can only take 1 CSE class each, between the four classes CSE 311, CSE 312, CSE 331, and CSE 332. Each student (independently of others) takes CSE 311 with probability 0.3, CSE 312 with probability 0.4, CSE 331 with probability 0.1, and CSE 332 with probability 0.2. What is the probability that exactly 31 sign up for CSE 311, 39 sign up for CSE 312, 7 sign up for CSE 331, and 23 sign up for CSE 332
Answer:
[tex]P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Step-by-step explanation:
Sample space, n = 100
Let the number of students signed up for CSE 311 = a
Let the number of students signed up for CSE 312 = b
Let the number of students signed up for CSE 331 = c
Let the number of students signed up for CSE 332 = d
Probability of taking CSE 311, [tex]P_a[/tex] = 0.3
Probability of taking CSE 312, [tex]P_b[/tex] = 0.4
Probability of taking CSE 331, [tex]P_c[/tex] = 0.1
Probability of taking CSE 332, [tex]P_d[/tex] = 0.2
[tex]P(a,b,c,d) = \frac{n!}{a! b! c! d!} p_a^{a} p_b^{b} p_c^{c} p_d^{d} \\P(a=31,b=39,c=7,d=23) = \frac{100!}{31! 39! 7! 23!} * 0.3^{31} * 0.4^{39} * 0.1^{7} 0.2^{23}\\P(a=31,b=39,c=7,d=23) = \frac{4.58*10^{111}}{2.13*10^{56}* 5040 }* (1.57*10^{-55})\\P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
6 out of 9 pairs of your jeans are blue. What percentage of you
jeans are NOT blue?
Answer:
33.333333%
Step-by-step explanation:
If 6/9 (66.66666666%) of the jeans are blue it means that 3/9 of the jeans are not blue. 3/9 as a percentage is 33.333333%
Answer:
33.3%
Step-by-step explanation:
6 ÷ 9 = 66.66666667%
100% - 66.66666667% = 33.3% (Or you can put 33.33333333)
Hope this helped! :)
WILL GIVE BRAINLIEST! Match the equations that are the same
Answer:
1. 1/x = 8
Answer = 8x-1
2. 8x+1=3
Answer ; x=1/4
3. 7= 14/X
Answer ; x = 2
4.1/2x^2 = 2
Answer ;x=2
Step-by-step explanation:
[tex]\frac{1}{x} =8 \\8x = 1\\\\\\8x+1=3\\Collect -like- terms \\8x =3-1\\8x = 2\\Divide -both -sides- by ;8\\\frac{8x}{8} =\frac{2}{8} \\x = 1/4\\\\\\7= \frac{14}{x} \\Cross -multiply\\7x =14\\Divide-both-sides-by-7\\x = 2\\\\\\\frac{1}{2} x^{2} =2\\\frac{x^{2} }{2} =2\\Cross-multiply\\x^{2} =4\\Squre-root -both-sides\\\sqrt{x^2}=\sqrt{4} \\x = 2\\[/tex]
Answer:
1. 1/x=8 ⇒ 8x= 1
2. 8x+1= 3⇒ x=1/4
3. 7= 14/x ⇒ x =2
4. 1/2x^2= 2 ⇒ x=2 this is a repeat of one above
None is matching x=1/2
Couple more! Running out of time lol!
Answer:
A translation; (x,y) --> (x-4,y-5)
Step-by-step explanation:
This is because the figures are congruent and in the same orientation but just in different locations on the coordinate plane.
A(0,3) --> A'(-4,-2)
So, the rule is (x,y) --> (x-4,y-5)
If the area to the left of x in a normal distribution is 0.187, what is the area to the right of x? (Enter an exact number as an integer, fraction, or decimal.)
Answer:
Area to the right is 0.813
Step-by-step explanation:
Since the area under the full normal distribution should render "1" (one), then the area to the right of x should be:
1 - area to the left of x = 1 - 0.187 = 0.813
The area to the right of x in this normal distribution will be 0.813.
What is a normal distribution?The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean.
The probabilities for values that are farther from the mean taper off equally in both directions. Extreme values in the distribution's two tails are likewise rare.
Not all symmetrical distributions are normal, even though the normal distribution is symmetrical.
We know that the total area described in a normal distribution is 1.
Given, that the area to the left of x in a normal distribution is 0.187.
So, the area to the right of x will be,
1 - 0.187.
= 0.813.
learn more about normal distribution here :
https://brainly.com/question/15103234
#SPJ2
Which best describes thermal energy?
Answer:
It's the third Answer: It is the portion of internal energy that can be transferred from one substance to another.
Hope this helps
Answer:
c
Step-by-step explanation:
Factor by grouping 5x^3+6x^2+25x+30
Answer:
(5x + 6) (x² + 5)
Step-by-step explanation:
5x³ + 6x² + 25x + 30
= x² (5x + 6) + 25x + 30 -- Group 5x³ and 6x²
= x² (5x + 6) + 5 (5x + 6) -- Group 25x and 30
= (5x + 6) (x² + 5) -- Both terms have a common factor of 5x + 6
An equilateral triangular plate with sides 6 m is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s^2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m^3.) rhog^3(3)^1/2 _______ dx = _______ N
Answer:
26,400 N
Step-by-step explanation:
PLEASE CHECK ATTACHMENT FOR COMPLETE SOLUTION
Tom takes a cancer test and the test is advertised as being 99% accurate: if you have cancer you will test positive 99% of the time, and if you don't have cancer, you will test negative 99% of the time. If 1% of all people have cancer and Tom tests positive, what is the prob that Tom has the disease
Answer:
99% chance tommy has it
Step-by-step explanation:
cuz do da math
Sphere A has a diameter of 2 and is dilated by a scale factor of 3 to create sphere B. What is the ratio of the volume of sphere A to sphere B? 2:6 4:36 1:3 1:27
Answer:
1:27 (D)
Step-by-step explanation:
Given:
Sphere A has a diameter of 2
Sphere A is dilated to create sphere B
Scale factor = 3
Volume of a sphere = 4/3 πr³
Radius = r = diameter/2 = 2/2
r = 1
Volume of sphere A = 4/3 ×π(1)³
Volume of sphere A = 4/3 × π
Volume of sphere B = 4/3 πR³
Since the diameter was dilated, the diameter of B = diameter of A × scale factor
diameter of B = 2×3 = 6
Radius of B = R = diameter/2 = 3
Volume of sphere B = 4/3 × π(3)³
Volume of sphere B = (4/3)(27)π
Ratio of the volume of sphere A to volume of sphere B
= [4/3 ×π]: [(4/3)(27)π]
= (4π/3)/[(4π/3)×27] = 1/27
= 1:27
Answer: 1:27
Step-by-step explanation:
The original volume * scale factor cubed = new volume.
The scale factor is 3 and 3^3 is 27, so the ratio is 1:27
Marking Brainliest! 3(x-100)=?
Answer:
3x - 300
Step-by-step explanation:
Expand the brackets or use distribute law.
Answer:
[tex]3x - 300[/tex]solution,
[tex]3(x - 100) \\ = 3 \times x - 3 \times 100 \\ = 3x - 300[/tex]
hope this helps..
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps. This system of equations models the given information for both stamp types. x – y = 34 x + y = 212
Step-by-step explanation:
x - y = 34
x + y = 212
2x = 246
x = 123
123 + y = 212
y = 89
(123, 89)
look at the figure shown below
Answer:
Answer is given below with explanations.
Step-by-step explanation:
Answer is option 1) 85 : 51
[tex]given \: that \: \\ triangle \: SPT \: is \: similar \: to \: triangle \: QPR \\ corresponding \: sides \: of \: similar \: \\ triangles \: are \: in \: proportion \\ then \: \\ \frac{SP}{ QP} = \frac{PT }{ PR} \\ \frac{3x}{3x + 24} = \frac{51}{85} \\ taking \: reciprocal \: on \: both \: sides \\ \frac{3x + 24}{3x} = \frac{85}{51} [/tex]
Option 1 is correct.
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
Help! Just a little more
Answer:
x = 7
y = 8
Step-by-step explanation:
4y-4 = 28
4y = 32
y = 8
10x+65 = 135
10x = 70
x = 7
Answer:
Step-by-step explanation:
(4y-4)=28
4y=32
y=8
(10x+65)=135
10x=70
x=7
Find the equation for the parabola that has its vertex at the origin and has directrix at x=1/48
Answer:
The equation for a parabola with vertex at the origin and a directrix at x = 1/48 is [tex]x= \frac{1}{12}\cdot y^{2}[/tex].
Step-by-step explanation:
As directrix is a vertical line, the parabola must "horizontal" and increasing in the -x direction. Then, the standard equation for such geometric construction centered at (h, k) is:
[tex]x - h = 4\cdot p \cdot (y-k)^{2}[/tex]
Where:
[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the location of vertex with respect to origin, dimensionless.
[tex]p[/tex] - Least distance of directrix with respect to vertex, dimensionless.
Since vertex is located at the origin and horizontal coordinate of the directrix, least distance of directrix is positive. That is:
[tex]p = x_{D} - x_{V}[/tex]
[tex]p = \frac{1}{48}-0[/tex]
[tex]p = \frac{1}{48}[/tex]
Now, the equation for a parabola with vertex at the origin and a directrix at x = 1/48 is [tex]x= \frac{1}{12}\cdot y^{2}[/tex].
Progress
Question ID: 470099
One student can paint a wall in 12 minutes. Another student can paint the same wall in 24 minutes. Working together, how long will it
take for them to paint the wall?
Answer:
8 minStep-by-step explanation:
Try this:
1 wall 1 288
------------------------ = --------------- = --------------- min = 8 min
1 wall 1 wall 24 + 12 36
(---------) + (---------) ------------
12 min 24 min 288
is lmn congruent to opq if so name the postulate
Answer:
Option (A)
Step-by-step explanation:
Given:
LM ≅ OP
MN ≅ PQ
∠M ≅ ∠P
To Prove:
ΔLMN ≅ ΔOQP
Statements Reasons
1). LM ≅ OP 1). Given
2). MN ≅ PQ 2). Given
3). ∠P ≅ ∠M 3). Given
4). ΔLNM ≅ ΔOQP 4). By the SAS postulate of congruence.
[Side - Angle - Side]
Therefore, Option (A) will be the answer.
"There is a group of people. The average height of these people is 67 inches. Is it more likely to pick an individual who is more than 68 inches tall or a sample of four people who average more than 68 inches tall
Answer:
Step-by-step explanation:
The spread of the height of each person in the group depends on the standard deviation. A low standard deviation means that the heights are closer to the mean than that of a high standard deviation. If an individual is picked, the probability of picking one who is more than 68 inches tall is small as this depends on the number of individuals in this category. The probability of picking a sample of four people who average more than 68 inches tall would be higher since average would be taken. Therefore, it is more likely to pick a sample of four people who average more than 68 inches tall
circumference of 6cm ? help plz <3 heyyy b a e (bet you won't reply :)
Answer:
If r = 6 cm, the the circumference is c = 2π(6) = 12π cm
HOPE THIS HELPS AND PLS MARK AS BRAINLIEST
THNXX :)