The scores of a high school entrance exam are approximately normally distributed with a given mean Mu = 82.4 and standard deviation Sigma = 3.3. What percentage of the scores are between 75.8 and 89?
Notice that
75.8 = 82.4 - 6.6 = 82.4 - 2 × 3.3
89 = 82.4 + 6.6 = 82.4 + 2 × 3.3
Then the percentage of students with scores between 75.8 and 89 make up the part of the distribution that lies within 2 standard deviations of the mean. The empirical (68-95-99.7) rule says that approximately 95% of any distribution lies within this range.
Answer:
b
Step-by-step explanation:
If x = 1, y = 7, and z = 15, determine a number that when added to x, y, and z yields
consecutive terms of a geometric sequence. What are the first three terms in the
geometric sequence?
Answer:
The first three terms in the geometric sequence are 18, 24, 32.
Step-by-step explanation:
A number when added to [tex]x,y,z[/tex] that yields consecutive terms of a geometric sequence is an unknown number [tex]t\in \mathbb{Z}[/tex]
Given
[tex]x = 1, y = 7, z = 15[/tex]
We know
[tex]\alpha _1 = 1+t[/tex]
[tex]\alpha _2 = 7+t[/tex]
[tex]\alpha _3 = 15+t[/tex]
Recall that a geometric sequence is in the form
[tex]\boxed{a_n = a_1 \cdot r^{n-1}}[/tex]
Therefore, once [tex]\alpha_1, \alpha_2, \alpha_1[/tex] are consecutive terms,
[tex]15+t = (1+t) r^{3-1} \implies 15+t = (1+t) r^2[/tex]
To find the ratio, for
[tex]\dots a_{k-1}, a_k, a_{k+1} \dots[/tex]
we know
[tex]\dfrac{a_k}{a_{k-1}} =\dfrac{a_k}{a_{k-1}} =r[/tex]
Therefore,
[tex]\dfrac{(7+t)}{(1+t)} =\dfrac{(15+t)}{(7+t)} \implies (7+t)^2 = (15+t)(1+t)[/tex]
[tex]\implies 49+14t+t^2=15+16t+t^2 \implies -2t=-34 \implies t=17[/tex]
The ratio is therefore
[tex]r=\dfrac{4}{3}[/tex]
Therefore, the first three terms in the geometric sequence are 18, 24, 32.
Geometry please help me!In the figure below, what value of x will satisfy the midsegment theorea? X=
Answer:
x=30.5
Step-by-step explanation:
Using midsegment 's theorea:
[tex]2=\dfrac{RG}{RS} =\dfrac{RH}{RQ} =\dfrac{GH}{SQ} \\\\4x-65=2x-4\\\\2x=61\\\\x=\dfrac{61}{2} \\\\x=30.5\\[/tex]
Which is the same length as 4 kilometers?
Answer:
A. 4000 meters because
1 km = 1000 meters
and 4 km = 1000 × 4 = 4000
............
(x - 7)2 = x2 - 49
O True
O False
Answer:
False
Step-by-step explanation:
Which of the following behaviors would best describe someone who is listening and paying attention? a) Leaning toward the speaker O b) Interrupting the speaker to share their opinion c) Avoiding eye contact d) Asking questions to make sure they understand what's being said
The answer is A and D
good luck
51: Y = 3: 5 value of Y
Answer:Y=25:3
Step-by-step explanation:
Answer:
51 : 85 = 3 : 5Step-by-step explanation:
51 : Y = 3 : 551 ÷ 17 = 3•To find the Y we should multiply 5 by 17 5 × 17 = 8551 : 85 = 3 : 5•Checking51 ÷ 17 = 3 ; 85 ÷ 17 = 5[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Which of the following functions has order 2 rotational symmetry about the same origin?
The answer is "Option B", and the further explanation can be defined as follows:
A rectangle is symmetrical in 2 ways. In particular, it has two-order rotational symmetry (RS2).If an object rotates 360 degrees, it's an ordering of symmetrical is the number of times it appears to be the same.There are three levels of matching: Order 2 if only two times, Order 3 if three matches are made, and so forth.The wrong choice can be defined as follows:
In option a and c, both are wrong because it has no rotational symmetry.In option d, it is wrong because it downs the diagram on the negative (x,y) axis.Therefore, "Option B" is correct and its diagram is defined in the attached file.
Learn more:
2 rotational symmetry: brainly.com/question/1531736
Find the distance between the two points (1.5,2.7) and (3.5,4.3) given in polar coordinates and using radians.
Answer:
2.56
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(3.5 - 1.5)² + (4.3 - 2.7)²
√(2)² + (1.6)²
√(4) + (2.56)
√6.56
= 2.56
PLS HELP I DONT KNOW THIS ONE
Answer:
x+3
---------------
(x-3)(x-2)(x-4)
Step-by-step explanation:
x+4 x^2 -16
---------------÷ -------------
x^2 - 5x+6 x+3
Copy dot flip
x+4 x+3
--------------- * -------------
x^2 - 5x+6 x^2 -16
Factor
x+4 x+3
--------------- * -------------
(x-3)(x-2) (x-4)(x+4)
Cancel like terms
1 x+3
--------------- * -------------
(x-3)(x-2) (x-4)1
x+3
--------------- x cannot equal 3,2,4 -4
(x-3)(x-2)(x-4)
What is the measure of b, in degrees
Answer:
B) 32
Step-by-step explanation:
(sin 74) / 10 = (sin c) / 10
c = 74
180 - 74 -74
= 32
Need helpppp ! tyyy
Answer:
63°
Step-by-step explanation:
Both angle 3 and 2 are equal because of the property of vertically opposite angles.Last year, Rob set up the Road Runner Race for his school.
The race was 1,200 meters long and 188 people signed up to
run the race. 38 people did not show up to run. This year,
there will be 3 times as many runners as last year. How
many people will run the race this year?
Answer:
450 runners
Step-by-step explanation:
The product of x and its opposite is always 1.
O True
O False
Answer:
False
Step-by-step explanation:
x
The opposite of x is -x
x* -x = -x^2
This is not always 1
Answer:
false
Step-by-step explanation:
x*-x= - x ² so its not always 1
so I just started using brainly sorry if its not appropriate
2sin(2x) + 1 = 3sin(2x) Solve for x with exact answers. The domain is 0 ≤ x ≤ π
Answer:
x = π/4.
Step-by-step explanation:
3sin(2x) = 2sin(2x) + 1
3sin(2x) - 2sin(2x) = 1
1sin(2x) = 1
sin(2x) = 1
When a variable n = π/2, sin(π/2) = 1 [refer to the unit circle].
2x = π/2
x = π/4.
Hope this helps!
The Rogers family and the Brooks family each used their sprinklers last summer. The Rogers family's sprinkler was used for 30 hours. The Brooks family's sprinkler was used for 25 hours. There was a combined total output of 1775 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 65 L per hour?
Step-by-step explanation:
what happens if there is excess or deficit of proteins in our body
is y=x^2 a proportional relationship?
is y=2+x a proportional relationship?
is y=2/x a proportional relationship?
is y=2x a proportional relationship?
Answer:
is y=x^2 a proportional relationship?
[tex]{ \sf{yes. \: constant \: of \: proportionality = 1}}[/tex]
is y=2+x a proportional relationship?
[tex]{ \sf{no. \: unless \: y \: is \: proportinal \: to \: (2 + x)}}[/tex]
is y=2/x a proportional relationship?
[tex]{ \sf{yes. \: where \: proportianality \: constant \: is \: 2}}[/tex]
is y=2x a proportional relationship?
[tex]{ \sf{yeah. \: constant \: is \: 2}}[/tex]
X>70
y<45
What is the smallest whole number value of x - y?
Answer:
27
Step-by-step explanation:
x-y
We are subtracting and we want the smallest number
We want the smallest number for x and the largest number for y
The smallest number for x is 71
The largest number for y is 44
71-44
27
Charla has six segments with which to make two triangles. The segments lengths are 2 in., 3 in., 4 in., 5 in., 6 in., and 7 in. Which are possible side lengths of her two triangles?
2 in., 4 in., 6 in. and 3 in., 5 in., 7 in.
2 in., 5 in., 6 in. and 3 in., 4 in., 7 in.
2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.
2 in., 3 in., 6 in. and 4 in., 5 in., 7 in.
Answer:
The answer is option C
2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.
Step-by-step explanation:
Using only the digits 5, 6, 7, 8, how many different three digit numbers can beformed
Answer:
totally 16 numbers can be formed
It is hard and the condition of repeat of number should be clear if you have formula ( it is obvious to have) you can use that.
The table above shows some values of the functions f
and g. What is the value of f(g(1)) ?
A) 2
B) 3
C) 4
D) 5
Answer:
a
Step-by-step explanation:
g(1)=5
f(g(1))=f(5)
f(5)=2
A computer system uses passwords that are exactly six characters and each character is one of the 26 letters (a–z) or 10 integers (0–9). Suppose that 10,000 users of the system have unique passwords. A hacker randomly selects (with replace- ment) one billion passwords from the potential set, and a match to a user’s password is called a hit. (a) What is the distribution of the number of hits? (b) What is the probability of no hits? (c) What are the mean and variance of the number of hits?
Answer:
The number of hits would follow a binomial distribution with [tex]n =10,\!000[/tex] and [tex]p \approx 4.59 \times 10^{-6}[/tex].
The probability of finding [tex]0[/tex] hits is approximately [tex]0.955[/tex] (or equivalently, approximately [tex]95.5\%[/tex].)
The mean of the number of hits is approximately [tex]0.0459[/tex]. The variance of the number of hits is approximately [tex]0.0459\![/tex] (not the same number as the mean.)
Step-by-step explanation:
There are [tex](26 + 10)^{6} \approx 2.18 \times 10^{9}[/tex] possible passwords in this set. (Approximately two billion possible passwords.)
Each one of the [tex]10^{9}[/tex] randomly-selected passwords would have an approximately [tex]\displaystyle \frac{10,\!000}{2.18 \times 10^{9}}[/tex] chance of matching one of the users' password.
Denote that probability as [tex]p[/tex]:
[tex]p := \displaystyle \frac{10,\!000}{2.18 \times 10^{9}} \approx 4.59 \times 10^{-6}[/tex].
For any one of the [tex]10^{9}[/tex] randomly-selected passwords, let [tex]1[/tex] denote a hit and [tex]0[/tex] denote no hits. Using that notation, whether a selected password hits would follow a bernoulli distribution with [tex]p \approx 4.59 \times 10^{-6}[/tex] as the likelihood of success.
Sum these [tex]0[/tex]'s and [tex]1[/tex]'s over the set of the [tex]10^{9}[/tex] randomly-selected passwords, and the result would represent the total number of hits.
Assume that these [tex]10^{9}[/tex] randomly-selected passwords are sampled independently with repetition. Whether each selected password hits would be independent from one another.
Hence, the total number of hits would follow a binomial distribution with [tex]n = 10^{9}[/tex] trials (a billion trials) and [tex]p \approx 4.59 \times 10^{-6}[/tex] as the chance of success on any given trial.
The probability of getting no hit would be:
[tex](1 - p)^{n} \approx 7 \times 10^{-1996} \approx 0[/tex].
(Since [tex](1 - p)[/tex] is between [tex]0[/tex] and [tex]1[/tex], the value of [tex](1 - p)^{n}[/tex] would approach [tex]0\![/tex] as the value of [tex]n[/tex] approaches infinity.)
The mean of this binomial distribution would be:[tex]n\cdot p \approx (10^{9}) \times (4.59 \times 10^{-6}) \approx 0.0459[/tex].
The variance of this binomial distribution would be:
[tex]\begin{aligned}& n \cdot p \cdot (1 - p)\\ & \approx(10^{9}) \times (4.59 \times 10^{-6}) \times (1- 4.59 \times 10^{-6})\\ &\approx 4.59 \times 10^{-6}\end{aligned}[/tex].
The humidity is currently 56% and falling at a rate of 4 percentage points per hour. (a) Estimate the change in humidity over the next 20 minutes. (Round your answer to one decimal place.) -1.4 Incorrect: Your answer is incorrect. percentage points
Answer:
The change is of -1.3 percentage points.
Step-by-step explanation:
The humidity is currently 56% and falling at a rate of 4 percentage points per hour.
This means that after n hours the humidity is of:
[tex]H(n) = 56 - 4n[/tex]
Estimate the change in humidity over the next 20 minutes.
It currently is 56%.
20 minutes is 20/60 = 1/3 of an hours, so:
[tex]H(\frac{1}{3}) = 56 - 4\frac{1}{3} = 54.7[/tex]
Change:
54.7 - 56 = -1.3
The change is of -1.3 percentage points.
The change in humidity over the next 20 minutes falling at a rate of 4 percentage points per hour is -1.3.
The humidity is currently 56% and falling at a rate of 4 percentage points per hour.
What is the formula used to determine the change in humidity?The change is determined by the small about of humidity changes x to x+h, so the output of x+h is the value of f at x plus the approximate change in f, that is
[tex]\rm f(x+h) =f(x) + f'(x) \times h[/tex]
f(x)= 56%
20 minutes is 20/60 = 1/3 of an hours
So, The change in humidity is
[tex]f'(x) = 4 \times 1/3[/tex]
f'(x) = 1.3
Here, it is falling at the rate of 4% point per hour so we will take it as negative as -1.3.
Learn more about changes in humidity;
https://brainly.com/question/14363655
Alex purchased
1/2
of a gallon of milk. He put
2/11
of the milk in a smoothie. How much of a gallon of milk did Alex put in his smoothie?
Answer:
1/11 of a gallon
Step-by-step explanation:
He used 2/11 of 1/2 gallon
2/11 * 1/2 = 1/11 of a gallon
Answer:
[tex]\frac{1}{11}[/tex]
Step-by-step explanation:
Step 1: Find how much of a gallon he used
[tex]\frac{2}{11} * \frac{1}{2} =\frac{2}{22}[/tex]
[tex]\frac{2}{22}=\frac{1}{11}[/tex]
Answer: [tex]\frac{1}{11}[/tex]
Helppp!!!!!
Please!!!
{ is question #1 is right?? }
{ i need help with question #2 please }
Please!!
Helppp!!!!!
Answer:
fyi b's answer has imaginary numbers in it...
Imaginary: 1 +[tex]\frac{\sqrt{2i} }{2 }[/tex]
Imaginary: 1 - [tex]\frac{\sqrt{2i} }{2 }[/tex]
Step-by-step explanation:
[tex]2x^{2} - 4x -3 = 0[/tex]
[tex]\sqrt{-4^{2} -4(2)(3)}[/tex] = [tex]\sqrt{-8}[/tex] ... the negative root will produce imaginary solutions
9514 1404 393
Answer:
1a. -4, 3/4
1b. 1-0.71i, 1+0.71i
Step-by-step explanation:
The directions tell you to use the quadratic formula. Factoring may get you the solution somewhat more easily, but does not comply with the directions.
The quadratic formula tells you ...
[tex]\text{The solution to }ax^2+bx+c=0\text{ is given by }\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
__
1a. a=4, b=13, c=-12
[tex]x=\dfrac{-13\pm\sqrt{13^2-4(4)(-12)}}{2(4)}=\dfrac{-13\pm\sqrt{361}}{8}=\dfrac{-13\pm19}{8}\\\\x=\left\{-4,\dfrac{3}{4}\right\}[/tex]
__
1b. After adding 3 to both sides, a=2, b=-4, c=3
[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(2)(3)}}{2(2)}=\dfrac{4\pm\sqrt{-8}}{4}=1\pm\dfrac{\sqrt{2}}{2}i\\\\x=\left\{1-\dfrac{\sqrt{2}}{2}i,1+\dfrac{\sqrt{2}}{2}i\right\}\approx\{1-0.71i,1+0.71i\}[/tex]
what is the mean in 0.33, 0.33, 0.54, 0.46, 0.30, 0.77, 0.42, 0.44, 0.60, 0.32, 0.47, 0.64, 0.61, 0.69, 0.41, 0.39, 0.66, 0.60, 0.61, 0.70
Answer:
0.5145
Step-by-step explanation:
Mean is also known as average. It is expressed as:
Mean = Sum of data/Sample size
Sum of data = 0.33+0.33+0.54+0.46+0.30+0.77+0.42+0.44+0.60+0.32+0.47+0.64+0.61+0.69+0.41+0.39+0.66+0.60+0.61+0.70
Sum of data = 10.29
Sample size = 20
Mean = 10.29/20
Mean = 0.5145
Hence the mean of the data is 0.5145
A population of deer in Florida grows according to a logistic model, with r = 0.17 and K = 10,000. At what population size is the per capita population growth rate the highest? Group of answer choices N = 1000 N = 5000 N = 8000 N = 10000
Answer:
N = 1000
Step-by-step explanation:
The population growth of species per capita of any geographical can be computed by using the formula:
[tex]\dfrac{dN}{dT}=rN (1 - \dfrac{N}{K})[/tex]
here;
N = population chance
T = time taken
K = carrying capacity
r = the constant exponential growth rate
From the given equation, we can posit that the value of r will be the greatest at the time the value of dN is highest:
As such, when the population chance = 1000
[tex]\dfrac{dN}{dT}=0.17 * 1000 (1 - \dfrac{1000}{10000})[/tex]
[tex]\dfrac{dN}{dT}=0.17 * 1000 (0.9)[/tex]
[tex]\dfrac{dN}{dT}= 153[/tex]
At N = 5000;
[tex]\dfrac{dN}{dT}= 85[/tex]
At N= 8000;
[tex]\dfrac{dN}{dT}= 34[/tex]
At N = 10000
[tex]\dfrac{dN}{dT}= 0[/tex]
what is 5.5 feet in centimeters?
Answer:
167.64 cm
Step-by-step explanation:
I dont kno how to work it out
the x coordinates of the point 2y-x=10 intersect the line yaxis
Answer:
Point has co-ordinates, (0, 5)
Step-by-step explanation:
If they cut y-axis, then x = 0
[tex]2y - x = 10 \\ 2y - 0 = 10 \\ 2y = 10 \\ y = 5[/tex]
PLEASE ANSWER
For a parabola where p > 0, the curve will open
Options
To the left
Up
Down
To the right
Answer:
‼️D) To the right‼️
Explanation
There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.
